From 1aa87389b481d4c32c85b3741c3edf7c2437be71 Mon Sep 17 00:00:00 2001
From: pancetta <pancetta@users.noreply.github.com>
Date: Fri, 10 Nov 2023 07:01:41 +0000
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index e869f2e041d482461df85fe37a0d1f9cd65e8622..3014ae804c1c81250c2a64d8392f38f581fb5c36 100644
GIT binary patch
delta 29
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delta 29
hcmew{hvml{mJNshu^1T`7;ZlPPm&SBdh&k?9{|oN4Eg{7

diff --git a/.doctrees/projects/doc_fput.doctree b/.doctrees/projects/doc_fput.doctree
index 0f1440ee0cf6318a7c0f4c07e12b83bb64e21bd9..06ddb066c1ffd83aa2844711b8057fa8b03c92b3 100644
GIT binary patch
delta 37
kcmZ3ylyUJ=#tmVvEXKwb#*_aWi*C+$Wno0{dfdc$0Qk`iPyhe`

delta 37
kcmZ3ylyUJ=#tmVvEJg+fhLisri*C+$Wno0{dfdc$0QS=iGynhq

diff --git a/.doctrees/projects/doc_matrixPFASST_matrix.doctree b/.doctrees/projects/doc_matrixPFASST_matrix.doctree
index cec982742f6de45b5ed9cffd1993f7fd4abb7e17..6511a45b406604b0805bb0c8a464940548aca928 100644
GIT binary patch
delta 32
jcmX@{obkkS#tnPom<<fgH}8*&;Dj;~m^W8t`*8pO=i&^r

delta 32
jcmX@{obkkS#tnPom<<h$Ht&y%;Dj;~m^W8t`*8pO=V}bA

diff --git a/.doctrees/projects/matrixPFASST.doctree b/.doctrees/projects/matrixPFASST.doctree
index 50a4c1021dd7545076fbf9dee2cbc534eb2acfb2..2b8de2f00b2f881af8dd0209a09a3d8e48152d60 100644
GIT binary patch
delta 32
icmZoX$J}_1dBcVbW&=a>&3r`(%$tRCey~D$pGyGB+6)2!

delta 32
icmZoX$J}_1dBcVbW<x`x&3r`(%$tRCey~D$pGyGBb_@Cd

diff --git a/.doctrees/pySDC/implementations.convergence_controller_classes.inexactness.doctree b/.doctrees/pySDC/implementations.convergence_controller_classes.inexactness.doctree
index 015d26d9eec95e095af22c6eaf34b12e64e7a5ac..114b4c88933aaf961299061458c6e653921b8080 100644
GIT binary patch
delta 3487
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diff --git a/.doctrees/pySDC/implementations.problem_classes.AllenCahn_2D_FD.doctree b/.doctrees/pySDC/implementations.problem_classes.AllenCahn_2D_FD.doctree
index 2f0679eea71fb77c82e62e1a1a612bdfe3cd3462..65394d36bd56600435828beb5b94c1c86f3a9205 100644
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diff --git a/.doctrees/pySDC/implementations.problem_classes.Quench.doctree b/.doctrees/pySDC/implementations.problem_classes.Quench.doctree
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diff --git a/.doctrees/pySDC/implementations.problem_classes.polynomial_test_problem.doctree b/.doctrees/pySDC/implementations.problem_classes.polynomial_test_problem.doctree
index a87a818f0549127c512a435b386dcfd29afff3eb..737e3b319f8257c0c85f20d10621772bcd01f3f8 100644
GIT binary patch
delta 2850
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delta 85
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diff --git a/.doctrees/tutorial/doc_step_2_C.doctree b/.doctrees/tutorial/doc_step_2_C.doctree
index 4a755ff8b1a6f99d186b43ba02c9571aedc22291..abafd4dc3d8c60f2aad7e423d54d5494b9e32ae5 100644
GIT binary patch
delta 1384
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delta 1374
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diff --git a/.doctrees/tutorial/doc_step_3_B.doctree b/.doctrees/tutorial/doc_step_3_B.doctree
index 81fbaf50362ed2186f4e163475ff2f6b687197d6..a233eee0df0815f3ed4062b51432cb81291a64f4 100644
GIT binary patch
delta 802
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delta 800
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diff --git a/.doctrees/tutorial/doc_step_4_D.doctree b/.doctrees/tutorial/doc_step_4_D.doctree
index b294c8fac8c109f6c61ae8d8576a454f04d586ae..cceff9bf6b81f5ce33d941de46e0ca303cb923d9 100644
GIT binary patch
delta 101
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delta 101
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diff --git a/.doctrees/tutorial/doc_step_7_A.doctree b/.doctrees/tutorial/doc_step_7_A.doctree
index 085b57007698a8168060fa3bc76d67de73ddd93f..f33c19ab098190f38b741f2a8d2ac6a4ed38551f 100644
GIT binary patch
delta 181
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delta 187
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diff --git a/.doctrees/tutorial/doc_step_7_B.doctree b/.doctrees/tutorial/doc_step_7_B.doctree
index 1767ac084d7b20f9d33b0a5b5fb8b19672706262..60f5b62293c33b0e1bd2a586c07d6ec5e7a6ff19 100644
GIT binary patch
delta 179
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delta 177
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diff --git a/.doctrees/tutorial/doc_step_7_C.doctree b/.doctrees/tutorial/doc_step_7_C.doctree
index 52528921819e979750e468f671e01d743e9d2c14..a770520a542827db41e8337fc7391d2c9a57279c 100644
GIT binary patch
delta 135
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delta 135
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diff --git a/.doctrees/tutorial/doc_step_8_C.doctree b/.doctrees/tutorial/doc_step_8_C.doctree
index 58cafdf7ea49e86cb0407a6f29885259ee8933f7..d85125fc38a4bbb26abb7954c7e9c9583657b30a 100644
GIT binary patch
delta 304
zcmbQgiD~{OrVUSW`3+1h%`A)!Ee(Lc%*=AKVtc}7i^gqCeC9@$76yhUmOx-&Y7P|N
zw)t#f0u#Tnk)^4rnK4M*$lS<uvtqj_Ge1zRxv`~@F~}4{W02~^$)|clHvj5MWa2Y6
xFf}m%TVQEyWC4=fe5!W~&?G~13j-4)kV)p279fd;O?4-k2APvKKb>I30RUTiS+4*9

delta 304
zcmd5$yA8rX43$hnm8%#a8`wVQ&c_@Sl*s@TEPzB62`Lg%2FMCg4rK=-u>~wag|h{(
zeE(sBVS@2}a>S8il_DaNO6<$F&U&4pV5&$1B|{K4e$KCR4UWADj7BS=gj}|}jq{8_
zM0joSadkKS(jD^m)<7W`B8vrL@_t=t^3pxPsZt6=mO(`o6OPm634eAefA0J34<Kh*
AMF0Q*

diff --git a/.doctrees/tutorial/step_2.doctree b/.doctrees/tutorial/step_2.doctree
index 482a65a478499e47b928601107009ab8d8b09320..5ad21f50306ec72a41f613b283a7ac36dc969eb2 100644
GIT binary patch
delta 1396
zcmaEMf%(}5<_(MI@fsQ^7?@d^np&9}>KJd{Ft3;iRcNxo!YVY8z*V}NXB|x7zz|-F
zA)+_=`6+KSQTx-|_)u&$n!NCG<K%N|OwbhauieIvs?c(>;M&H?`q$+qd*|{_Zdk{G
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delta 1386
zcmaEMf%(}5<_(MI@fuhv7+6@Dm|Gc{=@@R_Ft3;iRcNxo!YVY8z*V}NXB|x7zz|-F
zA)+_=`6+KSQTx-|_)u&$n!NCG<K%N|OwbhauieIvs?c(>;M&H?`q$+qd*|{_Zdk{G
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cWU|{nVH8cHDHfD%M^o&eOtG6++}+0o09nqdQvd(}

diff --git a/.doctrees/tutorial/step_3.doctree b/.doctrees/tutorial/step_3.doctree
index 3eae8da3d2bbcb3376d134265a8666525eb81449..dc7404b105205a751c8253b7a71ca9abb49545fd 100644
GIT binary patch
delta 790
zcmaELnEBOV<_#w0{DuY!24+^KrdFngI_8$<n`L?nna~9%&*`tg5YuVa-t0Hw8#@*W
zoyqkxFif7T(~K%+VPHDBvAuCJ&n#mUGb{{^z~bjI#4RTa&fbEm*2oO3wx$iu3}a)k
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o=0IZ_Ctv6`L3Oz~NV)uE?nNgi|LPG&ksFN%y2rz2?nU?Q0STwxtN;K2

delta 786
zcmaELnEBOV<_#w0{05c^1{PK(=2k{#I%Wo@n`L?nna~8yCeP`wz!1}E*52$l;Tt;^
z37yIHGtf;oo2=7}CT3_dxv{-*GS4hyJ``6NO>Ss!ntXniF{;r<=92|yZ$T9^h8R)P
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tb)f~wn1;z0x=m1RwE!wtn9RNC#N=N+!l+tCV*!yO=@AQ?xfk8H2LStf-(CO!

diff --git a/.doctrees/tutorial/step_4.doctree b/.doctrees/tutorial/step_4.doctree
index 7ca1506a4417ed3b855236333372618577decc34..352b30ff743c219b00d7f80628c13b9634ed8dd0 100644
GIT binary patch
delta 101
zcmezRg8AzU<_*bD)l4jnEiH`|bafRJ6ioGu&5ezW4J=I{d^0^m3v&|#QzNs@j4vdZ
NCNF$$MZEeF9sskX8Y}<+

delta 101
zcmezRg8AzU<_*bD)r`#y3@yzSbafRJ6ioGujV;YgjVw$cd^0^m3u9ALBTMtmj4vdZ
NCNF$$MZEeF9ssi%8a4m`

diff --git a/.doctrees/tutorial/step_7.doctree b/.doctrees/tutorial/step_7.doctree
index 66ae4ef3ded402befe56fdd33e69438845ec1700..04bf136d9180726b9b58d269833febfd161c2b98 100644
GIT binary patch
delta 485
zcmccE$#SuiWka(Mv!Rjc<oyvclTR)bo!k&6JvlY>IkTaK@n-)pLq;|eJxdEq!^v9F
z#*-Vo<tASbf5v2Nxp{wtF(b2?x#?v8FqzGDfuf8|CYF;w`k8Kyjb;N%7#VH89PG?U
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a1+k3{L8>Qjc*{Py?7J9N1&c5K<OTqg1+y^#

delta 471
zcmccE$#SuiWka(Mvw^w!<oyvclTR)bo!k&6JvlY>IkS<O#b*C7Lq--;Jp<#(8qubc
z8@%NvUk`uAWNE&6e}pk3vx%kUWdAUk&2@pIKvkw@=9{&mEg6}Ojm<Y-4t8dwzNu+3
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Sc*{Py?7J9N1&c5K<OTq_II3*`

diff --git a/.doctrees/tutorial/step_8.doctree b/.doctrees/tutorial/step_8.doctree
index 9737070f993fc0ec10cbfb70dedbec7e514108d7..b0e0dc2ec0cb64c47b306f32c6aeeeed8b16187f 100644
GIT binary patch
delta 324
zcmd6hu?@m75JhDtqJSvr*n#eR7yEo$&>&HvFc5XtAWDKO24ECuKuSl2?J4-}yZ`<z
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ybQ60_f|QhoIK<|*s0nNfc}56*x}U>tomGZCw3t*ZKBMEf`9Ac&J{LZfDyko?5mBcA

delta 314
zcmd6hu?@mN3`KR9h=!1K^lV`JoIBqZG)Pp4un!eQ)*uRyiUAk}Bt)c06jV4&f!p`~
z{~nrjXwu{Bo+AYcWefm-!iUAPYB!II%?V2sk5SJv)ys*g>V0BX=d0P;f}COkg@VBT
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EFHi|qi2wiq

diff --git a/_images/timings_SDC_variants_Fisher.png b/_images/timings_SDC_variants_Fisher.png
index 86cb9bc914d030d887123a756a2946605ce0d8a8..a37cb382e13d91c234d30eecf25f43a99c586252 100644
GIT binary patch
literal 9890
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diff --git a/_modules/implementations/convergence_controller_classes/estimate_extrapolation_error.html b/_modules/implementations/convergence_controller_classes/estimate_extrapolation_error.html
index 3f5bf5d65f..5477e03dcb 100644
--- a/_modules/implementations/convergence_controller_classes/estimate_extrapolation_error.html
+++ b/_modules/implementations/convergence_controller_classes/estimate_extrapolation_error.html
@@ -544,6 +544,8 @@ <h1>Source code for implementations.convergence_controller_classes.estimate_extr
         <span class="n">default_params</span> <span class="o">=</span> <span class="p">{</span>
             <span class="s1">&#39;Taylor_order&#39;</span><span class="p">:</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">num_nodes</span><span class="p">,</span>
             <span class="s1">&#39;n&#39;</span><span class="p">:</span> <span class="n">num_nodes</span><span class="p">,</span>
+            <span class="s1">&#39;recompute_coefficients&#39;</span><span class="p">:</span> <span class="kc">False</span><span class="p">,</span>
+            <span class="o">**</span><span class="n">params</span><span class="p">,</span>
         <span class="p">}</span>
 
         <span class="k">return</span> <span class="p">{</span><span class="o">**</span><span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">setup</span><span class="p">(</span><span class="n">controller</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span> <span class="n">description</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">),</span> <span class="o">**</span><span class="n">default_params</span><span class="p">}</span></div>
@@ -573,18 +575,21 @@ <h1>Source code for implementations.convergence_controller_classes.estimate_extr
         <span class="n">t_eval</span> <span class="o">=</span> <span class="n">S</span><span class="o">.</span><span class="n">time</span> <span class="o">+</span> <span class="n">nodes_</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
 
         <span class="n">dts</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">nodes_</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">nodes_</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o">-</span> <span class="n">nodes_</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">Taylor_order</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">nodes</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">Taylor_order</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nodes</span><span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nodes</span><span class="p">)</span>
 
         <span class="c1"># compute the extrapolation coefficients</span>
-        <span class="c1"># TODO: Maybe this can be reused</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">get_extrapolation_coefficients</span><span class="p">(</span><span class="n">nodes</span><span class="p">,</span> <span class="n">dts</span><span class="p">,</span> <span class="n">t_eval</span><span class="p">)</span>
+        <span class="k">if</span> <span class="kc">None</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">coeff</span><span class="o">.</span><span class="n">u</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">recompute_coefficients</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">get_extrapolation_coefficients</span><span class="p">(</span><span class="n">nodes</span><span class="p">,</span> <span class="n">dts</span><span class="p">,</span> <span class="n">t_eval</span><span class="p">)</span>
 
         <span class="c1"># compute the extrapolated solution</span>
+        <span class="k">if</span> <span class="n">lvl</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">lvl</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">lvl</span><span class="o">.</span><span class="n">prob</span><span class="o">.</span><span class="n">eval_f</span><span class="p">(</span><span class="n">lvl</span><span class="o">.</span><span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">lvl</span><span class="o">.</span><span class="n">time</span><span class="p">)</span>
+
         <span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">lvl</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">==</span> <span class="n">imex_mesh</span><span class="p">:</span>
-            <span class="n">f</span> <span class="o">=</span> <span class="p">[</span><span class="n">me</span><span class="o">.</span><span class="n">impl</span> <span class="o">+</span> <span class="n">me</span><span class="o">.</span><span class="n">expl</span> <span class="k">for</span> <span class="n">me</span> <span class="ow">in</span> <span class="n">lvl</span><span class="o">.</span><span class="n">f</span><span class="p">]</span>
+            <span class="n">f</span> <span class="o">=</span> <span class="p">[</span><span class="n">lvl</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">impl</span> <span class="o">+</span> <span class="n">lvl</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">expl</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">coeff</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="ow">and</span> <span class="n">lvl</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">else</span> <span class="mf">0.0</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">lvl</span><span class="o">.</span><span class="n">f</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)]</span>
         <span class="k">elif</span> <span class="nb">type</span><span class="p">(</span><span class="n">lvl</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">==</span> <span class="n">mesh</span><span class="p">:</span>
-            <span class="n">f</span> <span class="o">=</span> <span class="n">lvl</span><span class="o">.</span><span class="n">f</span>
+            <span class="n">f</span> <span class="o">=</span> <span class="p">[</span><span class="n">lvl</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">coeff</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">else</span> <span class="mf">0.0</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">lvl</span><span class="o">.</span><span class="n">f</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)]</span>
         <span class="k">else</span><span class="p">:</span>
             <span class="k">raise</span> <span class="n">DataError</span><span class="p">(</span>
                 <span class="sa">f</span><span class="s2">&quot;Unable to store f from datatype </span><span class="si">{</span><span class="nb">type</span><span class="p">(</span><span class="n">lvl</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="si">}</span><span class="s2">, extrapolation based error estimate only</span><span class="se">\</span>
@@ -594,7 +599,7 @@ <h1>Source code for implementations.convergence_controller_classes.estimate_extr
         <span class="c1"># compute the error with the weighted sum</span>
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="p">:</span>
             <span class="n">idx</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">rank</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">size</span>
-            <span class="n">sendbuf</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">coeff</span><span class="o">.</span><span class="n">u</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">*</span> <span class="n">lvl</span><span class="o">.</span><span class="n">u</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">coeff</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">*</span> <span class="n">lvl</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
+            <span class="n">sendbuf</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">coeff</span><span class="o">.</span><span class="n">u</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">*</span> <span class="n">lvl</span><span class="o">.</span><span class="n">u</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">coeff</span><span class="o">.</span><span class="n">f</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">*</span> <span class="n">f</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
             <span class="n">u_ex</span> <span class="o">=</span> <span class="n">lvl</span><span class="o">.</span><span class="n">prob</span><span class="o">.</span><span class="n">dtype_u</span><span class="p">(</span><span class="n">lvl</span><span class="o">.</span><span class="n">prob</span><span class="o">.</span><span class="n">init</span><span class="p">,</span> <span class="n">val</span><span class="o">=</span><span class="mf">0.0</span><span class="p">)</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">rank</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">size</span> <span class="o">-</span> <span class="mi">1</span> <span class="k">else</span> <span class="kc">None</span>
             <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">Reduce</span><span class="p">(</span><span class="n">sendbuf</span><span class="p">,</span> <span class="n">u_ex</span><span class="p">,</span> <span class="n">op</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">sum</span><span class="p">,</span> <span class="n">root</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">size</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
         <span class="k">else</span><span class="p">:</span>
diff --git a/_modules/implementations/convergence_controller_classes/inexactness.html b/_modules/implementations/convergence_controller_classes/inexactness.html
index 5ca750174f..7495a14d5d 100644
--- a/_modules/implementations/convergence_controller_classes/inexactness.html
+++ b/_modules/implementations/convergence_controller_classes/inexactness.html
@@ -67,8 +67,42 @@ <h1>Source code for implementations.convergence_controller_classes.inexactness</
             <span class="s2">&quot;ratio&quot;</span><span class="p">:</span> <span class="mf">1e-2</span><span class="p">,</span>
             <span class="s2">&quot;min_tol&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
             <span class="s2">&quot;max_tol&quot;</span><span class="p">:</span> <span class="mf">1e99</span><span class="p">,</span>
+            <span class="s2">&quot;maxiter&quot;</span><span class="p">:</span> <span class="kc">None</span><span class="p">,</span>
+            <span class="s2">&quot;use_e_tol&quot;</span><span class="p">:</span> <span class="s1">&#39;e_tol&#39;</span> <span class="ow">in</span> <span class="n">description</span><span class="p">[</span><span class="s1">&#39;level_params&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">keys</span><span class="p">(),</span>
+            <span class="s2">&quot;initial_tol&quot;</span><span class="p">:</span> <span class="mf">1e-3</span><span class="p">,</span>
+            <span class="o">**</span><span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">setup</span><span class="p">(</span><span class="n">controller</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span> <span class="n">description</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">),</span>
         <span class="p">}</span>
-        <span class="k">return</span> <span class="p">{</span><span class="o">**</span><span class="n">defaults</span><span class="p">,</span> <span class="o">**</span><span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">setup</span><span class="p">(</span><span class="n">controller</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span> <span class="n">description</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)}</span></div>
+        <span class="k">if</span> <span class="n">defaults</span><span class="p">[</span><span class="s1">&#39;maxiter&#39;</span><span class="p">]:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">set_maxiter</span><span class="p">(</span><span class="n">description</span><span class="p">,</span> <span class="n">defaults</span><span class="p">[</span><span class="s1">&#39;maxiter&#39;</span><span class="p">])</span>
+        <span class="k">return</span> <span class="n">defaults</span></div>
+
+
+<div class="viewcode-block" id="NewtonInexactness.dependencies">
+<a class="viewcode-back" href="../../../pySDC/implementations.convergence_controller_classes.inexactness.html#implementations.convergence_controller_classes.inexactness.NewtonInexactness.dependencies">[docs]</a>
+    <span class="k">def</span> <span class="nf">dependencies</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">controller</span><span class="p">,</span> <span class="n">description</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Load the embedded error estimator if needed.</span>
+
+<span class="sd">        Args:</span>
+<span class="sd">            controller (pySDC.Controller): The controller</span>
+<span class="sd">            description (dict): The description object used to instantiate the controller</span>
+
+<span class="sd">        Returns:</span>
+<span class="sd">            None</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">dependencies</span><span class="p">(</span><span class="n">controller</span><span class="p">,</span> <span class="n">description</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">use_e_tol</span><span class="p">:</span>
+            <span class="kn">from</span> <span class="nn">pySDC.implementations.convergence_controller_classes.estimate_embedded_error</span> <span class="kn">import</span> <span class="p">(</span>
+                <span class="n">EstimateEmbeddedError</span><span class="p">,</span>
+            <span class="p">)</span>
+
+            <span class="n">controller</span><span class="o">.</span><span class="n">add_convergence_controller</span><span class="p">(</span>
+                <span class="n">EstimateEmbeddedError</span><span class="p">,</span>
+                <span class="n">description</span><span class="o">=</span><span class="n">description</span><span class="p">,</span>
+            <span class="p">)</span>
+
+        <span class="k">return</span> <span class="kc">None</span></div>
 
 
 <div class="viewcode-block" id="NewtonInexactness.post_iteration_processing">
@@ -85,11 +119,27 @@ <h1>Source code for implementations.convergence_controller_classes.inexactness</
 <span class="sd">            None</span>
 <span class="sd">        &quot;&quot;&quot;</span>
         <span class="k">for</span> <span class="n">lvl</span> <span class="ow">in</span> <span class="n">step</span><span class="o">.</span><span class="n">levels</span><span class="p">:</span>
-            <span class="n">lvl</span><span class="o">.</span><span class="n">prob</span><span class="o">.</span><span class="n">newton_tol</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span>
-                <span class="p">[</span><span class="nb">min</span><span class="p">([</span><span class="n">lvl</span><span class="o">.</span><span class="n">status</span><span class="o">.</span><span class="n">residual</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">ratio</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">max_tol</span><span class="p">]),</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">min_tol</span><span class="p">]</span>
+            <span class="n">SDC_accuracy</span> <span class="o">=</span> <span class="p">(</span>
+                <span class="n">lvl</span><span class="o">.</span><span class="n">status</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;error_embedded_estimate&#39;</span><span class="p">,</span> <span class="n">lvl</span><span class="o">.</span><span class="n">status</span><span class="o">.</span><span class="n">residual</span><span class="p">)</span>
+                <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">use_e_tol</span>
+                <span class="k">else</span> <span class="n">lvl</span><span class="o">.</span><span class="n">status</span><span class="o">.</span><span class="n">residual</span>
             <span class="p">)</span>
+            <span class="n">SDC_accuracy</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">initial_tol</span> <span class="k">if</span> <span class="n">SDC_accuracy</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">SDC_accuracy</span>
+            <span class="n">tol</span> <span class="o">=</span> <span class="nb">max</span><span class="p">([</span><span class="nb">min</span><span class="p">([</span><span class="n">SDC_accuracy</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">ratio</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">max_tol</span><span class="p">]),</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">min_tol</span><span class="p">])</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">set_tolerance</span><span class="p">(</span><span class="n">lvl</span><span class="p">,</span> <span class="n">tol</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Changed tolerance to </span><span class="si">{</span><span class="n">tol</span><span class="si">:</span><span class="s1">.2e</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">,</span> <span class="n">step</span><span class="p">)</span></div>
+
+
+<div class="viewcode-block" id="NewtonInexactness.set_tolerance">
+<a class="viewcode-back" href="../../../pySDC/implementations.convergence_controller_classes.inexactness.html#implementations.convergence_controller_classes.inexactness.NewtonInexactness.set_tolerance">[docs]</a>
+    <span class="k">def</span> <span class="nf">set_tolerance</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">lvl</span><span class="p">,</span> <span class="n">tol</span><span class="p">):</span>
+        <span class="n">lvl</span><span class="o">.</span><span class="n">prob</span><span class="o">.</span><span class="n">newton_tol</span> <span class="o">=</span> <span class="n">tol</span></div>
+
 
-            <span class="bp">self</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Changed Newton tolerance to </span><span class="si">{</span><span class="n">lvl</span><span class="o">.</span><span class="n">prob</span><span class="o">.</span><span class="n">newton_tol</span><span class="si">:</span><span class="s1">.2e</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">,</span> <span class="n">step</span><span class="p">)</span></div>
+<div class="viewcode-block" id="NewtonInexactness.set_maxiter">
+<a class="viewcode-back" href="../../../pySDC/implementations.convergence_controller_classes.inexactness.html#implementations.convergence_controller_classes.inexactness.NewtonInexactness.set_maxiter">[docs]</a>
+    <span class="k">def</span> <span class="nf">set_maxiter</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">description</span><span class="p">,</span> <span class="n">maxiter</span><span class="p">):</span>
+        <span class="n">description</span><span class="p">[</span><span class="s1">&#39;problem_params&#39;</span><span class="p">][</span><span class="s1">&#39;newton_maxiter&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">maxiter</span></div>
 </div>
 
 </pre></div>
diff --git a/_modules/implementations/problem_classes/AllenCahn_2D_FD.html b/_modules/implementations/problem_classes/AllenCahn_2D_FD.html
index 166f830bba..c32348dc7a 100644
--- a/_modules/implementations/problem_classes/AllenCahn_2D_FD.html
+++ b/_modules/implementations/problem_classes/AllenCahn_2D_FD.html
@@ -42,7 +42,7 @@ <h1>Source code for implementations.problem_classes.AllenCahn_2D_FD</h1><div cla
 <span class="kn">from</span> <span class="nn">scipy.sparse.linalg</span> <span class="kn">import</span> <span class="n">cg</span>
 
 <span class="kn">from</span> <span class="nn">pySDC.core.Errors</span> <span class="kn">import</span> <span class="n">ParameterError</span><span class="p">,</span> <span class="n">ProblemError</span>
-<span class="kn">from</span> <span class="nn">pySDC.core.Problem</span> <span class="kn">import</span> <span class="n">ptype</span>
+<span class="kn">from</span> <span class="nn">pySDC.core.Problem</span> <span class="kn">import</span> <span class="n">ptype</span><span class="p">,</span> <span class="n">WorkCounter</span>
 <span class="kn">from</span> <span class="nn">pySDC.helpers</span> <span class="kn">import</span> <span class="n">problem_helper</span>
 <span class="kn">from</span> <span class="nn">pySDC.implementations.datatype_classes.mesh</span> <span class="kn">import</span> <span class="n">mesh</span><span class="p">,</span> <span class="n">imex_mesh</span><span class="p">,</span> <span class="n">comp2_mesh</span>
 
@@ -119,6 +119,7 @@ <h1>Source code for implementations.problem_classes.AllenCahn_2D_FD</h1><div cla
         <span class="n">newton_tol</span><span class="o">=</span><span class="mf">1e-12</span><span class="p">,</span>
         <span class="n">lin_tol</span><span class="o">=</span><span class="mf">1e-8</span><span class="p">,</span>
         <span class="n">lin_maxiter</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
+        <span class="n">inexact_linear_ratio</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
         <span class="n">radius</span><span class="o">=</span><span class="mf">0.25</span><span class="p">,</span>
         <span class="n">order</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
     <span class="p">):</span>
@@ -137,14 +138,19 @@ <h1>Source code for implementations.problem_classes.AllenCahn_2D_FD</h1><div cla
             <span class="s1">&#39;nvars&#39;</span><span class="p">,</span>
             <span class="s1">&#39;nu&#39;</span><span class="p">,</span>
             <span class="s1">&#39;eps&#39;</span><span class="p">,</span>
+            <span class="s1">&#39;radius&#39;</span><span class="p">,</span>
+            <span class="s1">&#39;order&#39;</span><span class="p">,</span>
+            <span class="n">localVars</span><span class="o">=</span><span class="nb">locals</span><span class="p">(),</span>
+            <span class="n">readOnly</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+        <span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_makeAttributeAndRegister</span><span class="p">(</span>
             <span class="s1">&#39;newton_maxiter&#39;</span><span class="p">,</span>
             <span class="s1">&#39;newton_tol&#39;</span><span class="p">,</span>
             <span class="s1">&#39;lin_tol&#39;</span><span class="p">,</span>
             <span class="s1">&#39;lin_maxiter&#39;</span><span class="p">,</span>
-            <span class="s1">&#39;radius&#39;</span><span class="p">,</span>
-            <span class="s1">&#39;order&#39;</span><span class="p">,</span>
+            <span class="s1">&#39;inexact_linear_ratio&#39;</span><span class="p">,</span>
             <span class="n">localVars</span><span class="o">=</span><span class="nb">locals</span><span class="p">(),</span>
-            <span class="n">readOnly</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+            <span class="n">readOnly</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
         <span class="p">)</span>
 
         <span class="c1"># compute dx and get discretization matrix A</span>
@@ -165,6 +171,10 @@ <h1>Source code for implementations.problem_classes.AllenCahn_2D_FD</h1><div cla
         <span class="bp">self</span><span class="o">.</span><span class="n">newton_ncalls</span> <span class="o">=</span> <span class="mi">0</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">lin_ncalls</span> <span class="o">=</span> <span class="mi">0</span>
 
+        <span class="bp">self</span><span class="o">.</span><span class="n">work_counters</span><span class="p">[</span><span class="s1">&#39;newton&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">WorkCounter</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">work_counters</span><span class="p">[</span><span class="s1">&#39;rhs&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">WorkCounter</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">work_counters</span><span class="p">[</span><span class="s1">&#39;linear&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">WorkCounter</span><span class="p">()</span>
+
     <span class="nd">@staticmethod</span>
     <span class="k">def</span> <span class="nf">__get_A</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">dx</span><span class="p">):</span>
 <span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
@@ -241,6 +251,10 @@ <h1>Source code for implementations.problem_classes.AllenCahn_2D_FD</h1><div cla
             <span class="c1"># if g is close to 0, then we are done</span>
             <span class="n">res</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span><span class="p">)</span>
 
+            <span class="c1"># do inexactness in the linear solver</span>
+            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">inexact_linear_ratio</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">lin_tol</span> <span class="o">=</span> <span class="n">res</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">inexact_linear_ratio</span>
+
             <span class="k">if</span> <span class="n">res</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">newton_tol</span><span class="p">:</span>
                 <span class="k">break</span>
 
@@ -249,11 +263,15 @@ <h1>Source code for implementations.problem_classes.AllenCahn_2D_FD</h1><div cla
 
             <span class="c1"># newton update: u1 = u0 - g/dg</span>
             <span class="c1"># u -= spsolve(dg, g)</span>
-            <span class="n">u</span> <span class="o">-=</span> <span class="n">cg</span><span class="p">(</span><span class="n">dg</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="n">x0</span><span class="o">=</span><span class="n">z</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">lin_tol</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mi">0</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+            <span class="n">u</span> <span class="o">-=</span> <span class="n">cg</span><span class="p">(</span>
+                <span class="n">dg</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="n">x0</span><span class="o">=</span><span class="n">z</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">lin_tol</span><span class="p">,</span> <span class="n">maxiter</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">lin_maxiter</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">callback</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">work_counters</span><span class="p">[</span><span class="s1">&#39;linear&#39;</span><span class="p">]</span>
+            <span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
             <span class="c1"># increase iteration count</span>
             <span class="n">n</span> <span class="o">+=</span> <span class="mi">1</span>
             <span class="c1"># print(n, res)</span>
 
+            <span class="bp">self</span><span class="o">.</span><span class="n">work_counters</span><span class="p">[</span><span class="s1">&#39;newton&#39;</span><span class="p">]()</span>
+
         <span class="c1"># if n == self.newton_maxiter:</span>
         <span class="c1">#     raise ProblemError(&#39;Newton did not converge after %i iterations, error is %s&#39; % (n, res))</span>
 
@@ -288,12 +306,13 @@ <h1>Source code for implementations.problem_classes.AllenCahn_2D_FD</h1><div cla
         <span class="n">v</span> <span class="o">=</span> <span class="n">u</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>
         <span class="n">f</span><span class="p">[:]</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="o">+</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">eps</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">v</span> <span class="o">*</span> <span class="p">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">v</span><span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">nu</span><span class="p">))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nvars</span><span class="p">)</span>
 
+        <span class="bp">self</span><span class="o">.</span><span class="n">work_counters</span><span class="p">[</span><span class="s1">&#39;rhs&#39;</span><span class="p">]()</span>
         <span class="k">return</span> <span class="n">f</span></div>
 
 
 <div class="viewcode-block" id="allencahn_fullyimplicit.u_exact">
 <a class="viewcode-back" href="../../../pySDC/implementations.problem_classes.AllenCahn_2D_FD.html#implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit.u_exact">[docs]</a>
-    <span class="k">def</span> <span class="nf">u_exact</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
+    <span class="k">def</span> <span class="nf">u_exact</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">u_init</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">t_init</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
 <span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Routine to compute the exact solution at time :math:`t`.</span>
 
@@ -307,13 +326,19 @@ <h1>Source code for implementations.problem_classes.AllenCahn_2D_FD</h1><div cla
 <span class="sd">        me : dtype_u</span>
 <span class="sd">            The exact solution.</span>
 <span class="sd">        &quot;&quot;&quot;</span>
-
-        <span class="k">assert</span> <span class="n">t</span> <span class="o">==</span> <span class="mi">0</span><span class="p">,</span> <span class="s1">&#39;ERROR: u_exact only valid for t=0&#39;</span>
         <span class="n">me</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dtype_u</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">init</span><span class="p">,</span> <span class="n">val</span><span class="o">=</span><span class="mf">0.0</span><span class="p">)</span>
-        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nvars</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
-            <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nvars</span><span class="p">[</span><span class="mi">1</span><span class="p">]):</span>
-                <span class="n">r2</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">xvalues</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">xvalues</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span>
-                <span class="n">me</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">tanh</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">radius</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">r2</span><span class="p">))</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">eps</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">t</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
+
+            <span class="k">def</span> <span class="nf">eval_rhs</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">u</span><span class="p">):</span>
+                <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">eval_f</span><span class="p">(</span><span class="n">u</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">init</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">t</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>
+
+            <span class="n">me</span><span class="p">[:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">generate_scipy_reference_solution</span><span class="p">(</span><span class="n">eval_rhs</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">u_init</span><span class="p">,</span> <span class="n">t_init</span><span class="p">)</span>
+
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nvars</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
+                <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nvars</span><span class="p">[</span><span class="mi">1</span><span class="p">]):</span>
+                    <span class="n">r2</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">xvalues</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">xvalues</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span>
+                    <span class="n">me</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">tanh</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">radius</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">r2</span><span class="p">))</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">eps</span><span class="p">))</span>
 
         <span class="k">return</span> <span class="n">me</span></div>
 </div>
@@ -365,6 +390,7 @@ <h1>Source code for implementations.problem_classes.AllenCahn_2D_FD</h1><div cla
         <span class="n">f</span><span class="o">.</span><span class="n">impl</span><span class="p">[:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">v</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nvars</span><span class="p">)</span>
         <span class="n">f</span><span class="o">.</span><span class="n">expl</span><span class="p">[:]</span> <span class="o">=</span> <span class="p">(</span><span class="mf">1.0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">eps</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">v</span> <span class="o">*</span> <span class="p">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">v</span><span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">nu</span><span class="p">))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nvars</span><span class="p">)</span>
 
+        <span class="bp">self</span><span class="o">.</span><span class="n">work_counters</span><span class="p">[</span><span class="s1">&#39;rhs&#39;</span><span class="p">]()</span>
         <span class="k">return</span> <span class="n">f</span></div>
 
 
@@ -396,6 +422,7 @@ <h1>Source code for implementations.problem_classes.AllenCahn_2D_FD</h1><div cla
 
         <span class="k">def</span> <span class="nf">callback</span><span class="p">(</span><span class="n">xk</span><span class="p">):</span>
             <span class="n">context</span><span class="o">.</span><span class="n">num_iter</span> <span class="o">+=</span> <span class="mi">1</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">work_counters</span><span class="p">[</span><span class="s1">&#39;linear&#39;</span><span class="p">]()</span>
             <span class="k">return</span> <span class="n">context</span><span class="o">.</span><span class="n">num_iter</span>
 
         <span class="n">me</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dtype_u</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">init</span><span class="p">)</span>
@@ -416,6 +443,35 @@ <h1>Source code for implementations.problem_classes.AllenCahn_2D_FD</h1><div cla
         <span class="bp">self</span><span class="o">.</span><span class="n">lin_itercount</span> <span class="o">+=</span> <span class="n">context</span><span class="o">.</span><span class="n">num_iter</span>
 
         <span class="k">return</span> <span class="n">me</span></div>
+
+
+<div class="viewcode-block" id="allencahn_semiimplicit.u_exact">
+<a class="viewcode-back" href="../../../pySDC/implementations.problem_classes.AllenCahn_2D_FD.html#implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit.u_exact">[docs]</a>
+    <span class="k">def</span> <span class="nf">u_exact</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">u_init</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">t_init</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Routine to compute the exact solution at time t.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        t : float</span>
+<span class="sd">            Time of the exact solution.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        me : dtype_u</span>
+<span class="sd">            The exact solution.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">me</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dtype_u</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">init</span><span class="p">,</span> <span class="n">val</span><span class="o">=</span><span class="mf">0.0</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">t</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
+
+            <span class="k">def</span> <span class="nf">eval_rhs</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">u</span><span class="p">):</span>
+                <span class="n">f</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">eval_f</span><span class="p">(</span><span class="n">u</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">init</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">t</span><span class="p">)</span>
+                <span class="k">return</span> <span class="p">(</span><span class="n">f</span><span class="o">.</span><span class="n">impl</span> <span class="o">+</span> <span class="n">f</span><span class="o">.</span><span class="n">expl</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>
+
+            <span class="n">me</span><span class="p">[:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">generate_scipy_reference_solution</span><span class="p">(</span><span class="n">eval_rhs</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">u_init</span><span class="p">,</span> <span class="n">t_init</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">me</span><span class="p">[:]</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">u_exact</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">u_init</span><span class="p">,</span> <span class="n">t_init</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">me</span></div>
 </div>
 
 
diff --git a/_modules/implementations/problem_classes/Quench.html b/_modules/implementations/problem_classes/Quench.html
index fb1a716306..eed164bfd5 100644
--- a/_modules/implementations/problem_classes/Quench.html
+++ b/_modules/implementations/problem_classes/Quench.html
@@ -101,6 +101,10 @@ <h1>Source code for implementations.problem_classes.Quench</h1><div class="highl
 <span class="sd">        Maximum number of linear iterations inside the Newton solver.</span>
 <span class="sd">    direct_solver : bool, optional</span>
 <span class="sd">        Indicates if a direct solver should be used.</span>
+<span class="sd">    inexact_linear_ratio : float, optional</span>
+<span class="sd">        Ratio of tolerance of linear solver to the Newton residual, overrides `lintol`</span>
+<span class="sd">    min_lintol : float, optional</span>
+<span class="sd">        Minimal tolerance for the linear solver</span>
 <span class="sd">    reference_sol_type : str, optional</span>
 <span class="sd">        Indicates which method should be used to compute a reference solution.</span>
 <span class="sd">        Choose between ``&#39;scipy&#39;``, ``&#39;SDC&#39;``, or ``&#39;DIRK&#39;``.</span>
@@ -147,6 +151,7 @@ <h1>Source code for implementations.problem_classes.Quench</h1><div class="highl
         <span class="n">liniter</span><span class="o">=</span><span class="mi">99</span><span class="p">,</span>
         <span class="n">direct_solver</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
         <span class="n">inexact_linear_ratio</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+        <span class="n">min_lintol</span><span class="o">=</span><span class="mf">1e-12</span><span class="p">,</span>
         <span class="n">reference_sol_type</span><span class="o">=</span><span class="s1">&#39;scipy&#39;</span><span class="p">,</span>
     <span class="p">):</span>
 <span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
@@ -183,6 +188,7 @@ <h1>Source code for implementations.problem_classes.Quench</h1><div class="highl
             <span class="s1">&#39;lintol&#39;</span><span class="p">,</span>
             <span class="s1">&#39;liniter&#39;</span><span class="p">,</span>
             <span class="s1">&#39;inexact_linear_ratio&#39;</span><span class="p">,</span>
+            <span class="s1">&#39;min_lintol&#39;</span><span class="p">,</span>
             <span class="n">localVars</span><span class="o">=</span><span class="nb">locals</span><span class="p">(),</span>
             <span class="n">readOnly</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
         <span class="p">)</span>
@@ -359,11 +365,11 @@ <h1>Source code for implementations.problem_classes.Quench</h1><div class="highl
         <span class="n">u</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dtype_u</span><span class="p">(</span><span class="n">u0</span><span class="p">)</span>
         <span class="n">res</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span>
         <span class="n">delta</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dtype_u</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">init</span><span class="p">,</span> <span class="n">val</span><span class="o">=</span><span class="mf">0.0</span><span class="p">)</span>
-        <span class="n">z</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dtype_u</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">init</span><span class="p">,</span> <span class="n">val</span><span class="o">=</span><span class="mf">0.0</span><span class="p">)</span>
 
         <span class="c1"># construct a preconditioner for the space solver</span>
         <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">direct_solver</span><span class="p">:</span>
             <span class="n">M</span> <span class="o">=</span> <span class="n">inv</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">Id</span> <span class="o">-</span> <span class="n">factor</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">)</span><span class="o">.</span><span class="n">toarray</span><span class="p">())</span>
+            <span class="n">zero</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dtype_u</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">init</span><span class="p">,</span> <span class="n">val</span><span class="o">=</span><span class="mf">0.0</span><span class="p">)</span>
 
         <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">newton_maxiter</span><span class="p">):</span>
             <span class="c1"># assemble G such that G(u) = 0 at the solution of the step</span>
@@ -377,7 +383,7 @@ <h1>Source code for implementations.problem_classes.Quench</h1><div class="highl
                 <span class="k">break</span>
 
             <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">inexact_linear_ratio</span><span class="p">:</span>
-                <span class="bp">self</span><span class="o">.</span><span class="n">lintol</span> <span class="o">=</span> <span class="nb">max</span><span class="p">([</span><span class="n">res</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">inexact_linear_ratio</span><span class="p">,</span> <span class="mf">1e-12</span><span class="p">])</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">lintol</span> <span class="o">=</span> <span class="nb">max</span><span class="p">([</span><span class="n">res</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">inexact_linear_ratio</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">min_lintol</span><span class="p">])</span>
 
             <span class="c1"># assemble Jacobian J of G</span>
             <span class="n">J</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Id</span> <span class="o">-</span> <span class="n">factor</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">A</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_non_linear_Jacobian</span><span class="p">(</span><span class="n">u</span><span class="p">))</span>
@@ -389,7 +395,7 @@ <h1>Source code for implementations.problem_classes.Quench</h1><div class="highl
                 <span class="n">delta</span><span class="p">,</span> <span class="n">info</span> <span class="o">=</span> <span class="n">gmres</span><span class="p">(</span>
                     <span class="n">J</span><span class="p">,</span>
                     <span class="n">G</span><span class="p">,</span>
-                    <span class="n">x0</span><span class="o">=</span><span class="n">z</span><span class="p">,</span>
+                    <span class="n">x0</span><span class="o">=</span><span class="n">zero</span><span class="p">,</span>
                     <span class="n">M</span><span class="o">=</span><span class="n">M</span><span class="p">,</span>
                     <span class="n">tol</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">lintol</span><span class="p">,</span>
                     <span class="n">maxiter</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">liniter</span><span class="p">,</span>
diff --git a/_modules/implementations/problem_classes/polynomial_test_problem.html b/_modules/implementations/problem_classes/polynomial_test_problem.html
index b0a2bde42a..0993e56946 100644
--- a/_modules/implementations/problem_classes/polynomial_test_problem.html
+++ b/_modules/implementations/problem_classes/polynomial_test_problem.html
@@ -40,7 +40,7 @@ <h1>Source code for implementations.problem_classes.polynomial_test_problem</h1>
 <span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 
 <span class="kn">from</span> <span class="nn">pySDC.core.Problem</span> <span class="kn">import</span> <span class="n">ptype</span>
-<span class="kn">from</span> <span class="nn">pySDC.implementations.datatype_classes.mesh</span> <span class="kn">import</span> <span class="n">mesh</span>
+<span class="kn">from</span> <span class="nn">pySDC.implementations.datatype_classes.mesh</span> <span class="kn">import</span> <span class="n">mesh</span><span class="p">,</span> <span class="n">imex_mesh</span>
 
 
 <div class="viewcode-block" id="polynomial_testequation">
@@ -139,6 +139,44 @@ <h1>Source code for implementations.problem_classes.polynomial_test_problem</h1>
         <span class="k">return</span> <span class="n">me</span></div>
 </div>
 
+
+
+<div class="viewcode-block" id="polynomial_testequation_IMEX">
+<a class="viewcode-back" href="../../../pySDC/implementations.problem_classes.polynomial_test_problem.html#implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX">[docs]</a>
+<span class="k">class</span> <span class="nc">polynomial_testequation_IMEX</span><span class="p">(</span><span class="n">polynomial_testequation</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    IMEX version of the polynomial test problem that assigns half the derivative to the implicit part and the other half to the explicit part.</span>
+<span class="sd">    Keep in mind that you still cannot Really perform any solves.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">dtype_f</span> <span class="o">=</span> <span class="n">imex_mesh</span>
+
+<div class="viewcode-block" id="polynomial_testequation_IMEX.eval_f">
+<a class="viewcode-back" href="../../../pySDC/implementations.problem_classes.polynomial_test_problem.html#implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX.eval_f">[docs]</a>
+    <span class="k">def</span> <span class="nf">eval_f</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Derivative of the polynomial.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        u : dtype_u</span>
+<span class="sd">            Current values of the numerical solution.</span>
+<span class="sd">        t : float</span>
+<span class="sd">            Current time of the numerical solution is computed.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        f : dtype_f</span>
+<span class="sd">            The right-hand side of the problem.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">f</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dtype_f</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">init</span><span class="p">)</span>
+        <span class="n">derivative</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">poly</span><span class="o">.</span><span class="n">deriv</span><span class="p">(</span><span class="n">m</span><span class="o">=</span><span class="mi">1</span><span class="p">)(</span><span class="n">t</span><span class="p">)</span>
+        <span class="n">f</span><span class="o">.</span><span class="n">impl</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">derivative</span> <span class="o">/</span> <span class="mi">2</span>
+        <span class="n">f</span><span class="o">.</span><span class="n">expl</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">derivative</span> <span class="o">/</span> <span class="mi">2</span>
+        <span class="k">return</span> <span class="n">f</span></div>
+</div>
+
 </pre></div>
 
             <div class="clearer"></div>
diff --git a/coverage/coverage-badge.svg b/coverage/coverage-badge.svg
index 3be25f96b5..960ad446fd 100644
--- a/coverage/coverage-badge.svg
+++ b/coverage/coverage-badge.svg
@@ -1 +1 @@
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\ No newline at end of file
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="114" height="20" role="img" aria-label="coverage: 74.08%"><title>coverage: 74.08%</title><linearGradient id="s" x2="0" y2="100%"><stop offset="0" stop-color="#bbb" stop-opacity=".1"/><stop offset="1" stop-opacity=".1"/></linearGradient><clipPath id="r"><rect width="114" height="20" rx="3" fill="#fff"/></clipPath><g clip-path="url(#r)"><rect width="61" height="20" fill="#555"/><rect x="61" width="53" height="20" fill="#fe7d37"/><rect width="114" height="20" fill="url(#s)"/></g><g fill="#fff" text-anchor="middle" font-family="Verdana,Geneva,DejaVu Sans,sans-serif" text-rendering="geometricPrecision" font-size="110"><text aria-hidden="true" x="315" y="150" fill="#010101" fill-opacity=".3" transform="scale(.1)" textLength="510">coverage</text><text x="315" y="140" transform="scale(.1)" fill="#fff" textLength="510">coverage</text><text aria-hidden="true" x="865" y="150" fill="#010101" fill-opacity=".3" transform="scale(.1)" textLength="430">74.08%</text><text x="865" y="140" transform="scale(.1)" fill="#fff" textLength="430">74.08%</text></g></svg>
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diff --git a/coverage/d_020efe120a771d8a_fput_py.html b/coverage/d_020efe120a771d8a_fput_py.html
index dc1777b0b7..e8e16519b3 100644
--- a/coverage/d_020efe120a771d8a_fput_py.html
+++ b/coverage/d_020efe120a771d8a_fput_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_020efe120a771d8a_hamiltonian_and_energy_output_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -328,7 +328,7 @@ <h2>
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             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_020efe120a771d8a_hamiltonian_and_energy_output_py.html b/coverage/d_020efe120a771d8a_hamiltonian_and_energy_output_py.html
index a6571696b0..28212068cd 100644
--- a/coverage/d_020efe120a771d8a_hamiltonian_and_energy_output_py.html
+++ b/coverage/d_020efe120a771d8a_hamiltonian_and_energy_output_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_020efe120a771d8a_hamiltonian_output_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -196,7 +196,7 @@ <h2>
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             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_020efe120a771d8a_hamiltonian_output_py.html b/coverage/d_020efe120a771d8a_hamiltonian_output_py.html
index 69bbc0dbeb..9e5a99d232 100644
--- a/coverage/d_020efe120a771d8a_hamiltonian_output_py.html
+++ b/coverage/d_020efe120a771d8a_hamiltonian_output_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_020efe120a771d8a_harmonic_oscillator_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -170,7 +170,7 @@ <h2>
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             &nbsp; &nbsp; &nbsp;
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_020efe120a771d8a_harmonic_oscillator_py.html b/coverage/d_020efe120a771d8a_harmonic_oscillator_py.html
index caa5a6ae05..bd4bdb59b1 100644
--- a/coverage/d_020efe120a771d8a_harmonic_oscillator_py.html
+++ b/coverage/d_020efe120a771d8a_harmonic_oscillator_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_020efe120a771d8a_simple_problems_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -254,7 +254,7 @@ <h2>
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_020efe120a771d8a_simple_problems_py.html b/coverage/d_020efe120a771d8a_simple_problems_py.html
index 9048d47dfe..eb3cbd6d6c 100644
--- a/coverage/d_020efe120a771d8a_simple_problems_py.html
+++ b/coverage/d_020efe120a771d8a_simple_problems_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_020efe120a771d8a_solar_system_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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index 3457ef5693..4ce5b8222e 100644
--- a/coverage/d_020efe120a771d8a_solar_system_py.html
+++ b/coverage/d_020efe120a771d8a_solar_system_py.html
@@ -65,7 +65,7 @@ <h2>
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+            created at 2023-11-10 06:59 +0000
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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index abe7b3b0e8..6df48a39a1 100644
--- a/coverage/d_020efe120a771d8a_stop_at_error_hook_py.html
+++ b/coverage/d_020efe120a771d8a_stop_at_error_hook_py.html
@@ -65,7 +65,7 @@ <h2>
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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index b707e64473..aeeb40b083 100644
--- a/coverage/d_064a9f2a35945611_FaultHooks_py.html
+++ b/coverage/d_064a9f2a35945611_FaultHooks_py.html
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+            created at 2023-11-10 06:59 +0000
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             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
     </div>
 </footer>
diff --git a/coverage/d_5893b65af8042ae2_collocation_adaptivity_py.html b/coverage/d_5893b65af8042ae2_collocation_adaptivity_py.html
index f09dcfad1e..e06a2034e8 100644
--- a/coverage/d_5893b65af8042ae2_collocation_adaptivity_py.html
+++ b/coverage/d_5893b65af8042ae2_collocation_adaptivity_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_dahlquist_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -410,7 +410,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_dahlquist_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
     </div>
 </footer>
diff --git a/coverage/d_5893b65af8042ae2_dahlquist_py.html b/coverage/d_5893b65af8042ae2_dahlquist_py.html
index 86e386d9f7..c6bafe880b 100644
--- a/coverage/d_5893b65af8042ae2_dahlquist_py.html
+++ b/coverage/d_5893b65af8042ae2_dahlquist_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_extrapolation_within_Q_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -421,7 +421,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_extrapolation_within_Q_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
     </div>
 </footer>
diff --git a/coverage/d_5893b65af8042ae2_extrapolation_within_Q_py.html b/coverage/d_5893b65af8042ae2_extrapolation_within_Q_py.html
index 36230fb416..1253c15e50 100644
--- a/coverage/d_5893b65af8042ae2_extrapolation_within_Q_py.html
+++ b/coverage/d_5893b65af8042ae2_extrapolation_within_Q_py.html
@@ -2,7 +2,7 @@
 <html>
 <head>
     <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
-    <title>Coverage for pySDC/projects/Resilience/extrapolation_within_Q.py: 77%</title>
+    <title>Coverage for pySDC/projects/Resilience/extrapolation_within_Q.py: 0%</title>
     <link rel="icon" sizes="32x32" href="favicon_32.png">
     <link rel="stylesheet" href="style.css" type="text/css">
     <script type="text/javascript" src="coverage_html.js" defer></script>
@@ -12,7 +12,7 @@
     <div class="content">
         <h1>
             <span class="text">Coverage for </span><b>pySDC/projects/Resilience/extrapolation_within_Q.py</b>:
-            <span class="pc_cov">77%</span>
+            <span class="pc_cov">0%</span>
         </h1>
         <aside id="help_panel_wrapper">
             <input id="help_panel_state" type="checkbox">
@@ -55,8 +55,8 @@ <h1>
         </aside>
         <h2>
             <span class="text">53 statements &nbsp;</span>
-            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">41<span class="text"> run</span></button>
-            <button type="button" class="mis show_mis button_toggle_mis" value="mis" data-shortcut="m" title="Toggle lines missing">12<span class="text"> missing</span></button>
+            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">0<span class="text"> run</span></button>
+            <button type="button" class="mis show_mis button_toggle_mis" value="mis" data-shortcut="m" title="Toggle lines missing">53<span class="text"> missing</span></button>
             <button type="button" class="exc show_exc button_toggle_exc" value="exc" data-shortcut="x" title="Toggle lines excluded">2<span class="text"> excluded</span></button>
         </h2>
         <p class="text">
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_fault_injection_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -80,21 +80,21 @@ <h2>
     </div>
 </header>
 <main id="source">
-    <p class="run"><span class="n"><a id="t1" href="#t1">1</a></span><span class="t"><span class="key">import</span> <span class="nam">matplotlib</span><span class="op">.</span><span class="nam">pyplot</span> <span class="key">as</span> <span class="nam">plt</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t2" href="#t2">2</a></span><span class="t"><span class="key">import</span> <span class="nam">numpy</span> <span class="key">as</span> <span class="nam">np</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t1" href="#t1">1</a></span><span class="t"><span class="key">import</span> <span class="nam">matplotlib</span><span class="op">.</span><span class="nam">pyplot</span> <span class="key">as</span> <span class="nam">plt</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t2" href="#t2">2</a></span><span class="t"><span class="key">import</span> <span class="nam">numpy</span> <span class="key">as</span> <span class="nam">np</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t3" href="#t3">3</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t4" href="#t4">4</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">convergence_controller_classes</span><span class="op">.</span><span class="nam">estimate_extrapolation_error</span> <span class="key">import</span> <span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t4" href="#t4">4</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">convergence_controller_classes</span><span class="op">.</span><span class="nam">estimate_extrapolation_error</span> <span class="key">import</span> <span class="op">(</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t5" href="#t5">5</a></span><span class="t">    <span class="nam">EstimateExtrapolationErrorWithinQ</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t6" href="#t6">6</a></span><span class="t"><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t7" href="#t7">7</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">hooks</span><span class="op">.</span><span class="nam">log_errors</span> <span class="key">import</span> <span class="nam">LogLocalErrorPostStep</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t8" href="#t8">8</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">helpers</span><span class="op">.</span><span class="nam">stats_helper</span> <span class="key">import</span> <span class="nam">get_sorted</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t7" href="#t7">7</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">hooks</span><span class="op">.</span><span class="nam">log_errors</span> <span class="key">import</span> <span class="nam">LogLocalErrorPostStep</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t8" href="#t8">8</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">helpers</span><span class="op">.</span><span class="nam">stats_helper</span> <span class="key">import</span> <span class="nam">get_sorted</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t9" href="#t9">9</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t10" href="#t10">10</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">projects</span><span class="op">.</span><span class="nam">Resilience</span><span class="op">.</span><span class="nam">piline</span> <span class="key">import</span> <span class="nam">run_piline</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t11" href="#t11">11</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">projects</span><span class="op">.</span><span class="nam">Resilience</span><span class="op">.</span><span class="nam">advection</span> <span class="key">import</span> <span class="nam">run_advection</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t12" href="#t12">12</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">projects</span><span class="op">.</span><span class="nam">Resilience</span><span class="op">.</span><span class="nam">vdp</span> <span class="key">import</span> <span class="nam">run_vdp</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t10" href="#t10">10</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">projects</span><span class="op">.</span><span class="nam">Resilience</span><span class="op">.</span><span class="nam">piline</span> <span class="key">import</span> <span class="nam">run_piline</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t11" href="#t11">11</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">projects</span><span class="op">.</span><span class="nam">Resilience</span><span class="op">.</span><span class="nam">advection</span> <span class="key">import</span> <span class="nam">run_advection</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t12" href="#t12">12</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">projects</span><span class="op">.</span><span class="nam">Resilience</span><span class="op">.</span><span class="nam">vdp</span> <span class="key">import</span> <span class="nam">run_vdp</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t13" href="#t13">13</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t14" href="#t14">14</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t15" href="#t15">15</a></span><span class="t"><span class="key">def</span> <span class="nam">multiple_runs</span><span class="op">(</span><span class="nam">prob</span><span class="op">,</span> <span class="nam">dts</span><span class="op">,</span> <span class="nam">num_nodes</span><span class="op">,</span> <span class="nam">quad_type</span><span class="op">=</span><span class="str">'RADAU-RIGHT'</span><span class="op">,</span> <span class="nam">QI</span><span class="op">=</span><span class="str">'LU'</span><span class="op">,</span> <span class="nam">useMPI</span><span class="op">=</span><span class="key">False</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t15" href="#t15">15</a></span><span class="t"><span class="key">def</span> <span class="nam">multiple_runs</span><span class="op">(</span><span class="nam">prob</span><span class="op">,</span> <span class="nam">dts</span><span class="op">,</span> <span class="nam">num_nodes</span><span class="op">,</span> <span class="nam">quad_type</span><span class="op">=</span><span class="str">'RADAU-RIGHT'</span><span class="op">,</span> <span class="nam">QI</span><span class="op">=</span><span class="str">'LU'</span><span class="op">,</span> <span class="nam">useMPI</span><span class="op">=</span><span class="key">False</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t16" href="#t16">16</a></span><span class="t">    <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t17" href="#t17">17</a></span><span class="t"><span class="str">    Make multiple runs of a specific problem and record vital error information</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t18" href="#t18">18</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
@@ -108,13 +108,13 @@ <h2>
     <p class="pln"><span class="n"><a id="t26" href="#t26">26</a></span><span class="t"><span class="str">        dict: Errors for multiple runs</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t27" href="#t27">27</a></span><span class="t"><span class="str">        int: Order of the collocation problem</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t28" href="#t28">28</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t29" href="#t29">29</a></span><span class="t">    <span class="nam">description</span> <span class="op">=</span> <span class="op">{</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t30" href="#t30">30</a></span><span class="t">    <span class="nam">description</span><span class="op">[</span><span class="str">'level_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'restol'</span><span class="op">:</span> <span class="num">1e-10</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t31" href="#t31">31</a></span><span class="t">    <span class="nam">description</span><span class="op">[</span><span class="str">'step_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'maxiter'</span><span class="op">:</span> <span class="num">99</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t32" href="#t32">32</a></span><span class="t">    <span class="nam">description</span><span class="op">[</span><span class="str">'sweeper_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'num_nodes'</span><span class="op">:</span> <span class="nam">num_nodes</span><span class="op">,</span> <span class="str">'quad_type'</span><span class="op">:</span> <span class="nam">quad_type</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t33" href="#t33">33</a></span><span class="t">    <span class="nam">description</span><span class="op">[</span><span class="str">'convergence_controllers'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="nam">EstimateExtrapolationErrorWithinQ</span><span class="op">:</span> <span class="op">{</span><span class="op">}</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t29" href="#t29">29</a></span><span class="t">    <span class="nam">description</span> <span class="op">=</span> <span class="op">{</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t30" href="#t30">30</a></span><span class="t">    <span class="nam">description</span><span class="op">[</span><span class="str">'level_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'restol'</span><span class="op">:</span> <span class="num">1e-10</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t31" href="#t31">31</a></span><span class="t">    <span class="nam">description</span><span class="op">[</span><span class="str">'step_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'maxiter'</span><span class="op">:</span> <span class="num">99</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t32" href="#t32">32</a></span><span class="t">    <span class="nam">description</span><span class="op">[</span><span class="str">'sweeper_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'num_nodes'</span><span class="op">:</span> <span class="nam">num_nodes</span><span class="op">,</span> <span class="str">'quad_type'</span><span class="op">:</span> <span class="nam">quad_type</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t33" href="#t33">33</a></span><span class="t">    <span class="nam">description</span><span class="op">[</span><span class="str">'convergence_controllers'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="nam">EstimateExtrapolationErrorWithinQ</span><span class="op">:</span> <span class="op">{</span><span class="op">}</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t34" href="#t34">34</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t35" href="#t35">35</a></span><span class="t">    <span class="key">if</span> <span class="nam">useMPI</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t35" href="#t35">35</a></span><span class="t">    <span class="key">if</span> <span class="nam">useMPI</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
     <p class="mis show_mis"><span class="n"><a id="t36" href="#t36">36</a></span><span class="t">        <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">sweeper_classes</span><span class="op">.</span><span class="nam">generic_implicit_MPI</span> <span class="key">import</span> <span class="nam">generic_implicit_MPI</span><span class="op">,</span> <span class="nam">MPI</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t37" href="#t37">37</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
     <p class="mis show_mis"><span class="n"><a id="t38" href="#t38">38</a></span><span class="t">        <span class="nam">description</span><span class="op">[</span><span class="str">'sweeper_class'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">generic_implicit_MPI</span>&nbsp;</span><span class="r"></span></p>
@@ -122,25 +122,25 @@ <h2>
     <p class="mis show_mis"><span class="n"><a id="t40" href="#t40">40</a></span><span class="t">        <span class="key">if</span> <span class="nam">MPI</span><span class="op">.</span><span class="nam">COMM_WORLD</span><span class="op">.</span><span class="nam">rank</span> <span class="op">></span> <span class="nam">num_nodes</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
     <p class="mis show_mis"><span class="n"><a id="t41" href="#t41">41</a></span><span class="t">            <span class="key">return</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t42" href="#t42">42</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t43" href="#t43">43</a></span><span class="t">    <span class="key">if</span> <span class="nam">prob</span><span class="op">.</span><span class="nam">__name__</span> <span class="op">==</span> <span class="str">'run_advection'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t44" href="#t44">44</a></span><span class="t">        <span class="nam">description</span><span class="op">[</span><span class="str">'problem_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'order'</span><span class="op">:</span> <span class="num">6</span><span class="op">,</span> <span class="str">'stencil_type'</span><span class="op">:</span> <span class="str">'center'</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t43" href="#t43">43</a></span><span class="t">    <span class="key">if</span> <span class="nam">prob</span><span class="op">.</span><span class="nam">__name__</span> <span class="op">==</span> <span class="str">'run_advection'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t44" href="#t44">44</a></span><span class="t">        <span class="nam">description</span><span class="op">[</span><span class="str">'problem_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'order'</span><span class="op">:</span> <span class="num">6</span><span class="op">,</span> <span class="str">'stencil_type'</span><span class="op">:</span> <span class="str">'center'</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t45" href="#t45">45</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t46" href="#t46">46</a></span><span class="t">    <span class="nam">res</span> <span class="op">=</span> <span class="op">{</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t46" href="#t46">46</a></span><span class="t">    <span class="nam">res</span> <span class="op">=</span> <span class="op">{</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t47" href="#t47">47</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t48" href="#t48">48</a></span><span class="t">    <span class="key">for</span> <span class="nam">dt</span> <span class="key">in</span> <span class="nam">dts</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t49" href="#t49">49</a></span><span class="t">        <span class="nam">description</span><span class="op">[</span><span class="str">'level_params'</span><span class="op">]</span><span class="op">[</span><span class="str">'dt'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">dt</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t48" href="#t48">48</a></span><span class="t">    <span class="key">for</span> <span class="nam">dt</span> <span class="key">in</span> <span class="nam">dts</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t49" href="#t49">49</a></span><span class="t">        <span class="nam">description</span><span class="op">[</span><span class="str">'level_params'</span><span class="op">]</span><span class="op">[</span><span class="str">'dt'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">dt</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t50" href="#t50">50</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t51" href="#t51">51</a></span><span class="t">        <span class="nam">stats</span><span class="op">,</span> <span class="nam">controller</span><span class="op">,</span> <span class="nam">_</span> <span class="op">=</span> <span class="nam">prob</span><span class="op">(</span><span class="nam">custom_description</span><span class="op">=</span><span class="nam">description</span><span class="op">,</span> <span class="nam">Tend</span><span class="op">=</span><span class="num">5.0</span> <span class="op">*</span> <span class="nam">dt</span><span class="op">,</span> <span class="nam">hook_class</span><span class="op">=</span><span class="nam">LogLocalErrorPostStep</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t51" href="#t51">51</a></span><span class="t">        <span class="nam">stats</span><span class="op">,</span> <span class="nam">controller</span><span class="op">,</span> <span class="nam">_</span> <span class="op">=</span> <span class="nam">prob</span><span class="op">(</span><span class="nam">custom_description</span><span class="op">=</span><span class="nam">description</span><span class="op">,</span> <span class="nam">Tend</span><span class="op">=</span><span class="num">5.0</span> <span class="op">*</span> <span class="nam">dt</span><span class="op">,</span> <span class="nam">hook_class</span><span class="op">=</span><span class="nam">LogLocalErrorPostStep</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t52" href="#t52">52</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t53" href="#t53">53</a></span><span class="t">        <span class="nam">res</span><span class="op">[</span><span class="nam">dt</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t54" href="#t54">54</a></span><span class="t">        <span class="nam">res</span><span class="op">[</span><span class="nam">dt</span><span class="op">]</span><span class="op">[</span><span class="str">'e_loc'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">max</span><span class="op">(</span><span class="op">[</span><span class="nam">me</span><span class="op">[</span><span class="num">1</span><span class="op">]</span> <span class="key">for</span> <span class="nam">me</span> <span class="key">in</span> <span class="nam">get_sorted</span><span class="op">(</span><span class="nam">stats</span><span class="op">,</span> <span class="nam">type</span><span class="op">=</span><span class="str">'e_local_post_step'</span><span class="op">)</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t55" href="#t55">55</a></span><span class="t">        <span class="nam">res</span><span class="op">[</span><span class="nam">dt</span><span class="op">]</span><span class="op">[</span><span class="str">'e_ex'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">max</span><span class="op">(</span><span class="op">[</span><span class="nam">me</span><span class="op">[</span><span class="num">1</span><span class="op">]</span> <span class="key">for</span> <span class="nam">me</span> <span class="key">in</span> <span class="nam">get_sorted</span><span class="op">(</span><span class="nam">stats</span><span class="op">,</span> <span class="nam">type</span><span class="op">=</span><span class="str">'error_extrapolation_estimate'</span><span class="op">)</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t53" href="#t53">53</a></span><span class="t">        <span class="nam">res</span><span class="op">[</span><span class="nam">dt</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t54" href="#t54">54</a></span><span class="t">        <span class="nam">res</span><span class="op">[</span><span class="nam">dt</span><span class="op">]</span><span class="op">[</span><span class="str">'e_loc'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">max</span><span class="op">(</span><span class="op">[</span><span class="nam">me</span><span class="op">[</span><span class="num">1</span><span class="op">]</span> <span class="key">for</span> <span class="nam">me</span> <span class="key">in</span> <span class="nam">get_sorted</span><span class="op">(</span><span class="nam">stats</span><span class="op">,</span> <span class="nam">type</span><span class="op">=</span><span class="str">'e_local_post_step'</span><span class="op">)</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t55" href="#t55">55</a></span><span class="t">        <span class="nam">res</span><span class="op">[</span><span class="nam">dt</span><span class="op">]</span><span class="op">[</span><span class="str">'e_ex'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">max</span><span class="op">(</span><span class="op">[</span><span class="nam">me</span><span class="op">[</span><span class="num">1</span><span class="op">]</span> <span class="key">for</span> <span class="nam">me</span> <span class="key">in</span> <span class="nam">get_sorted</span><span class="op">(</span><span class="nam">stats</span><span class="op">,</span> <span class="nam">type</span><span class="op">=</span><span class="str">'error_extrapolation_estimate'</span><span class="op">)</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t56" href="#t56">56</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t57" href="#t57">57</a></span><span class="t">    <span class="nam">coll_order</span> <span class="op">=</span> <span class="nam">controller</span><span class="op">.</span><span class="nam">MS</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">.</span><span class="nam">levels</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">.</span><span class="nam">sweep</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">order</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t58" href="#t58">58</a></span><span class="t">    <span class="key">return</span> <span class="nam">res</span><span class="op">,</span> <span class="nam">coll_order</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t57" href="#t57">57</a></span><span class="t">    <span class="nam">coll_order</span> <span class="op">=</span> <span class="nam">controller</span><span class="op">.</span><span class="nam">MS</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">.</span><span class="nam">levels</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">.</span><span class="nam">sweep</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">order</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t58" href="#t58">58</a></span><span class="t">    <span class="key">return</span> <span class="nam">res</span><span class="op">,</span> <span class="nam">coll_order</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t59" href="#t59">59</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t60" href="#t60">60</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t61" href="#t61">61</a></span><span class="t"><span class="key">def</span> <span class="nam">plot_and_compute_order</span><span class="op">(</span><span class="nam">ax</span><span class="op">,</span> <span class="nam">res</span><span class="op">,</span> <span class="nam">num_nodes</span><span class="op">,</span> <span class="nam">coll_order</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t61" href="#t61">61</a></span><span class="t"><span class="key">def</span> <span class="nam">plot_and_compute_order</span><span class="op">(</span><span class="nam">ax</span><span class="op">,</span> <span class="nam">res</span><span class="op">,</span> <span class="nam">num_nodes</span><span class="op">,</span> <span class="nam">coll_order</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t62" href="#t62">62</a></span><span class="t">    <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t63" href="#t63">63</a></span><span class="t"><span class="str">    Plot and compute the order from the multiple runs ran with `multiple_runs`. Also, it is tested if the expected order</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t64" href="#t64">64</a></span><span class="t"><span class="str">    is reached for the respective errors.</span>&nbsp;</span><span class="r"></span></p>
@@ -154,33 +154,33 @@ <h2>
     <p class="pln"><span class="n"><a id="t72" href="#t72">72</a></span><span class="t"><span class="str">    Returns:</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t73" href="#t73">73</a></span><span class="t"><span class="str">        None</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t74" href="#t74">74</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t75" href="#t75">75</a></span><span class="t">    <span class="nam">dts</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">array</span><span class="op">(</span><span class="nam">list</span><span class="op">(</span><span class="nam">res</span><span class="op">.</span><span class="nam">keys</span><span class="op">(</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t76" href="#t76">76</a></span><span class="t">    <span class="nam">keys</span> <span class="op">=</span> <span class="nam">list</span><span class="op">(</span><span class="nam">res</span><span class="op">[</span><span class="nam">dts</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">]</span><span class="op">.</span><span class="nam">keys</span><span class="op">(</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t75" href="#t75">75</a></span><span class="t">    <span class="nam">dts</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">array</span><span class="op">(</span><span class="nam">list</span><span class="op">(</span><span class="nam">res</span><span class="op">.</span><span class="nam">keys</span><span class="op">(</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t76" href="#t76">76</a></span><span class="t">    <span class="nam">keys</span> <span class="op">=</span> <span class="nam">list</span><span class="op">(</span><span class="nam">res</span><span class="op">[</span><span class="nam">dts</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">]</span><span class="op">.</span><span class="nam">keys</span><span class="op">(</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t77" href="#t77">77</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t78" href="#t78">78</a></span><span class="t">    <span class="com"># local error is one order higher than global error</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t79" href="#t79">79</a></span><span class="t">    <span class="nam">expected_order</span> <span class="op">=</span> <span class="op">{</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t79" href="#t79">79</a></span><span class="t">    <span class="nam">expected_order</span> <span class="op">=</span> <span class="op">{</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t80" href="#t80">80</a></span><span class="t">        <span class="str">'e_loc'</span><span class="op">:</span> <span class="nam">coll_order</span> <span class="op">+</span> <span class="num">1</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t81" href="#t81">81</a></span><span class="t">        <span class="str">'e_ex'</span><span class="op">:</span> <span class="nam">num_nodes</span> <span class="op">+</span> <span class="num">1</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t82" href="#t82">82</a></span><span class="t">    <span class="op">}</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t83" href="#t83">83</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t84" href="#t84">84</a></span><span class="t">    <span class="key">for</span> <span class="nam">key</span> <span class="key">in</span> <span class="nam">keys</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t85" href="#t85">85</a></span><span class="t">        <span class="nam">errors</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">array</span><span class="op">(</span><span class="op">[</span><span class="nam">res</span><span class="op">[</span><span class="nam">dt</span><span class="op">]</span><span class="op">[</span><span class="nam">key</span><span class="op">]</span> <span class="key">for</span> <span class="nam">dt</span> <span class="key">in</span> <span class="nam">dts</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t84" href="#t84">84</a></span><span class="t">    <span class="key">for</span> <span class="nam">key</span> <span class="key">in</span> <span class="nam">keys</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t85" href="#t85">85</a></span><span class="t">        <span class="nam">errors</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">array</span><span class="op">(</span><span class="op">[</span><span class="nam">res</span><span class="op">[</span><span class="nam">dt</span><span class="op">]</span><span class="op">[</span><span class="nam">key</span><span class="op">]</span> <span class="key">for</span> <span class="nam">dt</span> <span class="key">in</span> <span class="nam">dts</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t86" href="#t86">86</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t87" href="#t87">87</a></span><span class="t">        <span class="nam">mask</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">logical_and</span><span class="op">(</span><span class="nam">errors</span> <span class="op">&lt;</span> <span class="num">1e-3</span><span class="op">,</span> <span class="nam">errors</span> <span class="op">></span> <span class="num">1e-10</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t88" href="#t88">88</a></span><span class="t">        <span class="nam">order</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">log</span><span class="op">(</span><span class="nam">errors</span><span class="op">[</span><span class="nam">mask</span><span class="op">]</span><span class="op">[</span><span class="num">1</span><span class="op">:</span><span class="op">]</span> <span class="op">/</span> <span class="nam">errors</span><span class="op">[</span><span class="nam">mask</span><span class="op">]</span><span class="op">[</span><span class="op">:</span><span class="op">-</span><span class="num">1</span><span class="op">]</span><span class="op">)</span> <span class="op">/</span> <span class="nam">np</span><span class="op">.</span><span class="nam">log</span><span class="op">(</span><span class="nam">dts</span><span class="op">[</span><span class="nam">mask</span><span class="op">]</span><span class="op">[</span><span class="num">1</span><span class="op">:</span><span class="op">]</span> <span class="op">/</span> <span class="nam">dts</span><span class="op">[</span><span class="nam">mask</span><span class="op">]</span><span class="op">[</span><span class="op">:</span><span class="op">-</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t87" href="#t87">87</a></span><span class="t">        <span class="nam">mask</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">logical_and</span><span class="op">(</span><span class="nam">errors</span> <span class="op">&lt;</span> <span class="num">1e-3</span><span class="op">,</span> <span class="nam">errors</span> <span class="op">></span> <span class="num">1e-10</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t88" href="#t88">88</a></span><span class="t">        <span class="nam">order</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">log</span><span class="op">(</span><span class="nam">errors</span><span class="op">[</span><span class="nam">mask</span><span class="op">]</span><span class="op">[</span><span class="num">1</span><span class="op">:</span><span class="op">]</span> <span class="op">/</span> <span class="nam">errors</span><span class="op">[</span><span class="nam">mask</span><span class="op">]</span><span class="op">[</span><span class="op">:</span><span class="op">-</span><span class="num">1</span><span class="op">]</span><span class="op">)</span> <span class="op">/</span> <span class="nam">np</span><span class="op">.</span><span class="nam">log</span><span class="op">(</span><span class="nam">dts</span><span class="op">[</span><span class="nam">mask</span><span class="op">]</span><span class="op">[</span><span class="num">1</span><span class="op">:</span><span class="op">]</span> <span class="op">/</span> <span class="nam">dts</span><span class="op">[</span><span class="nam">mask</span><span class="op">]</span><span class="op">[</span><span class="op">:</span><span class="op">-</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t89" href="#t89">89</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t90" href="#t90">90</a></span><span class="t">        <span class="key">if</span> <span class="nam">ax</span> <span class="key">is</span> <span class="key">not</span> <span class="key">None</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t90" href="#t90">90</a></span><span class="t">        <span class="key">if</span> <span class="nam">ax</span> <span class="key">is</span> <span class="key">not</span> <span class="key">None</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
     <p class="mis show_mis"><span class="n"><a id="t91" href="#t91">91</a></span><span class="t">            <span class="nam">ax</span><span class="op">.</span><span class="nam">loglog</span><span class="op">(</span><span class="nam">dts</span><span class="op">,</span> <span class="nam">errors</span><span class="op">,</span> <span class="nam">label</span><span class="op">=</span><span class="str">f'{key}: order={np.mean(order):.2f}'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t92" href="#t92">92</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t93" href="#t93">93</a></span><span class="t">        <span class="key">assert</span> <span class="nam">np</span><span class="op">.</span><span class="nam">isclose</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t93" href="#t93">93</a></span><span class="t">        <span class="key">assert</span> <span class="nam">np</span><span class="op">.</span><span class="nam">isclose</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t94" href="#t94">94</a></span><span class="t">            <span class="nam">np</span><span class="op">.</span><span class="nam">mean</span><span class="op">(</span><span class="nam">order</span><span class="op">)</span><span class="op">,</span> <span class="nam">expected_order</span><span class="op">[</span><span class="nam">key</span><span class="op">]</span><span class="op">,</span> <span class="nam">atol</span><span class="op">=</span><span class="num">0.5</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t95" href="#t95">95</a></span><span class="t">        <span class="op">)</span><span class="op">,</span> <span class="str">f'Expected order {expected_order[key]} for {key}, but got {np.mean(order):.2e}!'</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t96" href="#t96">96</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t97" href="#t97">97</a></span><span class="t">    <span class="key">if</span> <span class="nam">ax</span> <span class="key">is</span> <span class="key">not</span> <span class="key">None</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t97" href="#t97">97</a></span><span class="t">    <span class="key">if</span> <span class="nam">ax</span> <span class="key">is</span> <span class="key">not</span> <span class="key">None</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
     <p class="mis show_mis"><span class="n"><a id="t98" href="#t98">98</a></span><span class="t">        <span class="nam">ax</span><span class="op">.</span><span class="nam">legend</span><span class="op">(</span><span class="nam">frameon</span><span class="op">=</span><span class="key">False</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t99" href="#t99">99</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t100" href="#t100">100</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t101" href="#t101">101</a></span><span class="t"><span class="key">def</span> <span class="nam">check_order</span><span class="op">(</span><span class="nam">ax</span><span class="op">,</span> <span class="nam">prob</span><span class="op">,</span> <span class="nam">dts</span><span class="op">,</span> <span class="nam">num_nodes</span><span class="op">,</span> <span class="nam">quad_type</span><span class="op">,</span> <span class="op">**</span><span class="nam">kwargs</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t101" href="#t101">101</a></span><span class="t"><span class="key">def</span> <span class="nam">check_order</span><span class="op">(</span><span class="nam">ax</span><span class="op">,</span> <span class="nam">prob</span><span class="op">,</span> <span class="nam">dts</span><span class="op">,</span> <span class="nam">num_nodes</span><span class="op">,</span> <span class="nam">quad_type</span><span class="op">,</span> <span class="op">**</span><span class="nam">kwargs</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t102" href="#t102">102</a></span><span class="t">    <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t103" href="#t103">103</a></span><span class="t"><span class="str">    Check the order by calling `multiple_runs` and then `plot_and_compute_order`.</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t104" href="#t104">104</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
@@ -191,11 +191,11 @@ <h2>
     <p class="pln"><span class="n"><a id="t109" href="#t109">109</a></span><span class="t"><span class="str">        num_nodes (int): Number of nodes</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t110" href="#t110">110</a></span><span class="t"><span class="str">        quad_type (str): Type of nodes</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t111" href="#t111">111</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t112" href="#t112">112</a></span><span class="t">    <span class="nam">res</span><span class="op">,</span> <span class="nam">coll_order</span> <span class="op">=</span> <span class="nam">multiple_runs</span><span class="op">(</span><span class="nam">prob</span><span class="op">,</span> <span class="nam">dts</span><span class="op">,</span> <span class="nam">num_nodes</span><span class="op">,</span> <span class="nam">quad_type</span><span class="op">,</span> <span class="op">**</span><span class="nam">kwargs</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t113" href="#t113">113</a></span><span class="t">    <span class="nam">plot_and_compute_order</span><span class="op">(</span><span class="nam">ax</span><span class="op">,</span> <span class="nam">res</span><span class="op">,</span> <span class="nam">num_nodes</span><span class="op">,</span> <span class="nam">coll_order</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t112" href="#t112">112</a></span><span class="t">    <span class="nam">res</span><span class="op">,</span> <span class="nam">coll_order</span> <span class="op">=</span> <span class="nam">multiple_runs</span><span class="op">(</span><span class="nam">prob</span><span class="op">,</span> <span class="nam">dts</span><span class="op">,</span> <span class="nam">num_nodes</span><span class="op">,</span> <span class="nam">quad_type</span><span class="op">,</span> <span class="op">**</span><span class="nam">kwargs</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t113" href="#t113">113</a></span><span class="t">    <span class="nam">plot_and_compute_order</span><span class="op">(</span><span class="nam">ax</span><span class="op">,</span> <span class="nam">res</span><span class="op">,</span> <span class="nam">num_nodes</span><span class="op">,</span> <span class="nam">coll_order</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t114" href="#t114">114</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t115" href="#t115">115</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t116" href="#t116">116</a></span><span class="t"><span class="key">def</span> <span class="nam">main</span><span class="op">(</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t116" href="#t116">116</a></span><span class="t"><span class="key">def</span> <span class="nam">main</span><span class="op">(</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
     <p class="mis show_mis"><span class="n"><a id="t117" href="#t117">117</a></span><span class="t">    <span class="nam">fig</span><span class="op">,</span> <span class="nam">ax</span> <span class="op">=</span> <span class="nam">plt</span><span class="op">.</span><span class="nam">subplots</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="mis show_mis"><span class="n"><a id="t118" href="#t118">118</a></span><span class="t">    <span class="nam">num_nodes</span> <span class="op">=</span> <span class="num">3</span>&nbsp;</span><span class="r"></span></p>
     <p class="mis show_mis"><span class="n"><a id="t119" href="#t119">119</a></span><span class="t">    <span class="nam">quad_type</span> <span class="op">=</span> <span class="str">'RADAU-RIGHT'</span>&nbsp;</span><span class="r"></span></p>
@@ -214,7 +214,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_fault_injection_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_5893b65af8042ae2_fault_injection_py.html b/coverage/d_5893b65af8042ae2_fault_injection_py.html
index b2bbfc3aac..cd0c9b5363 100644
--- a/coverage/d_5893b65af8042ae2_fault_injection_py.html
+++ b/coverage/d_5893b65af8042ae2_fault_injection_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_fault_stats_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -669,7 +669,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_fault_stats_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_5893b65af8042ae2_fault_stats_py.html b/coverage/d_5893b65af8042ae2_fault_stats_py.html
index 288e5cda1d..9c30c69f57 100644
--- a/coverage/d_5893b65af8042ae2_fault_stats_py.html
+++ b/coverage/d_5893b65af8042ae2_fault_stats_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_heat_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -1807,7 +1807,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_heat_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_5893b65af8042ae2_heat_py.html b/coverage/d_5893b65af8042ae2_heat_py.html
index 7bdb8aed90..37a7999a4a 100644
--- a/coverage/d_5893b65af8042ae2_heat_py.html
+++ b/coverage/d_5893b65af8042ae2_heat_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_hook_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -194,7 +194,7 @@ <h2>
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             &nbsp; &nbsp; &nbsp;
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_5893b65af8042ae2_hook_py.html b/coverage/d_5893b65af8042ae2_hook_py.html
index e71ba11672..16098312f3 100644
--- a/coverage/d_5893b65af8042ae2_hook_py.html
+++ b/coverage/d_5893b65af8042ae2_hook_py.html
@@ -65,7 +65,7 @@ <h2>
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             &nbsp; &nbsp; &nbsp;
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -200,7 +200,7 @@ <h2>
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_5893b65af8042ae2_paper_plots_py.html b/coverage/d_5893b65af8042ae2_paper_plots_py.html
index 445ccfa69c..0872f47574 100644
--- a/coverage/d_5893b65af8042ae2_paper_plots_py.html
+++ b/coverage/d_5893b65af8042ae2_paper_plots_py.html
@@ -65,7 +65,7 @@ <h2>
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             &nbsp; &nbsp; &nbsp;
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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             &nbsp; &nbsp; &nbsp;
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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index 2c2c93bb9e..3d2d31e51b 100644
--- a/coverage/d_5893b65af8042ae2_piline_py.html
+++ b/coverage/d_5893b65af8042ae2_piline_py.html
@@ -65,7 +65,7 @@ <h2>
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+            created at 2023-11-10 06:59 +0000
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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index f0b4f396bc..9ae3e5e3e7 100644
--- a/coverage/d_5893b65af8042ae2_quench_py.html
+++ b/coverage/d_5893b65af8042ae2_quench_py.html
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             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
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             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -648,7 +648,7 @@ <h2>
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             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
     </div>
 </footer>
diff --git a/coverage/d_5893b65af8042ae2_strategies_py.html b/coverage/d_5893b65af8042ae2_strategies_py.html
index 01e3c4b367..9509d7ea6a 100644
--- a/coverage/d_5893b65af8042ae2_strategies_py.html
+++ b/coverage/d_5893b65af8042ae2_strategies_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_sweepers_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -1539,9 +1539,9 @@ <h2>
     <p class="pln"><span class="n"><a id="t1457" href="#t1457">1457</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
     <p class="run"><span class="n"><a id="t1458" href="#t1458">1458</a></span><span class="t">        <span class="key">if</span> <span class="nam">problem</span><span class="op">.</span><span class="nam">__name__</span> <span class="op">==</span> <span class="str">"run_vdp"</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
     <p class="run"><span class="n"><a id="t1459" href="#t1459">1459</a></span><span class="t">            <span class="key">if</span> <span class="nam">key</span> <span class="op">==</span> <span class="str">'work_newton'</span> <span class="key">and</span> <span class="nam">op</span> <span class="op">==</span> <span class="nam">sum</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t1460" href="#t1460">1460</a></span><span class="t">                <span class="key">return</span> <span class="num">2677</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t1460" href="#t1460">1460</a></span><span class="t">                <span class="key">return</span> <span class="num">3443</span>&nbsp;</span><span class="r"></span></p>
     <p class="run"><span class="n"><a id="t1461" href="#t1461">1461</a></span><span class="t">            <span class="key">elif</span> <span class="nam">key</span> <span class="op">==</span> <span class="str">'e_global_post_run'</span> <span class="key">and</span> <span class="nam">op</span> <span class="op">==</span> <span class="nam">max</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t1462" href="#t1462">1462</a></span><span class="t">                <span class="key">return</span> <span class="num">4.375184403937471e-06</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t1462" href="#t1462">1462</a></span><span class="t">                <span class="key">return</span> <span class="num">4.929282266752377e-06</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t1463" href="#t1463">1463</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
     <p class="exc show_exc"><span class="n"><a id="t1464" href="#t1464">1464</a></span><span class="t">        <span class="key">raise</span> <span class="nam">NotImplementedError</span><span class="op">(</span><span class="str">'The reference value you are looking for is not implemented for this strategy!'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
 </main>
@@ -1553,7 +1553,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_sweepers_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
     </div>
 </footer>
diff --git a/coverage/d_5893b65af8042ae2_sweepers_py.html b/coverage/d_5893b65af8042ae2_sweepers_py.html
index a61b1c2e04..05dd3cfe35 100644
--- a/coverage/d_5893b65af8042ae2_sweepers_py.html
+++ b/coverage/d_5893b65af8042ae2_sweepers_py.html
@@ -54,9 +54,9 @@ <h1>
             </div>
         </aside>
         <h2>
-            <span class="text">84 statements &nbsp;</span>
-            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">76<span class="text"> run</span></button>
-            <button type="button" class="mis show_mis button_toggle_mis" value="mis" data-shortcut="m" title="Toggle lines missing">8<span class="text"> missing</span></button>
+            <span class="text">103 statements &nbsp;</span>
+            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">93<span class="text"> run</span></button>
+            <button type="button" class="mis show_mis button_toggle_mis" value="mis" data-shortcut="m" title="Toggle lines missing">10<span class="text"> missing</span></button>
             <button type="button" class="exc show_exc button_toggle_exc" value="exc" data-shortcut="x" title="Toggle lines excluded">1<span class="text"> excluded</span></button>
         </h2>
         <p class="text">
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_5893b65af8042ae2_vdp_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -209,97 +209,127 @@ <h2>
     <p class="run"><span class="n"><a id="t127" href="#t127">127</a></span><span class="t">        <span class="key">return</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t128" href="#t128">128</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
     <p class="run"><span class="n"><a id="t129" href="#t129">129</a></span><span class="t">    <span class="key">def</span> <span class="nam">compute_residual</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">stage</span><span class="op">=</span><span class="str">''</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t130" href="#t130">130</a></span><span class="t">        <span class="key">if</span> <span class="nam">stage</span> <span class="key">not</span> <span class="key">in</span> <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">skip_residual_computation</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t131" href="#t131">131</a></span><span class="t">            <span class="nam">lvl</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">level</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t132" href="#t132">132</a></span><span class="t">            <span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span> <span class="op">=</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">prob</span><span class="op">.</span><span class="nam">eval_f</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span><span class="op">,</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">time</span> <span class="op">+</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">nodes</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t133" href="#t133">133</a></span><span class="t">        <span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">compute_residual</span><span class="op">(</span><span class="nam">stage</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t134" href="#t134">134</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t130" href="#t130">130</a></span><span class="t">        <span class="nam">lvl</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">level</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t131" href="#t131">131</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t132" href="#t132">132</a></span><span class="t">        <span class="key">if</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">residual_type</span><span class="op">[</span><span class="op">:</span><span class="num">4</span><span class="op">]</span> <span class="op">==</span> <span class="str">'full'</span> <span class="key">or</span> <span class="nam">stage</span> <span class="key">in</span> <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">skip_residual_computation</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t133" href="#t133">133</a></span><span class="t">            <span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">compute_residual</span><span class="op">(</span><span class="nam">stage</span><span class="op">=</span><span class="nam">stage</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t134" href="#t134">134</a></span><span class="t">            <span class="key">return</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t135" href="#t135">135</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t136" href="#t136">136</a></span><span class="t"><span class="key">class</span> <span class="nam">imex_1st_order_efficient</span><span class="op">(</span><span class="nam">efficient_sweeper</span><span class="op">,</span> <span class="nam">imex_1st_order</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t137" href="#t137">137</a></span><span class="t">    <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t138" href="#t138">138</a></span><span class="t"><span class="str">    Duplicate of `imex_1st_order` sweeper which is slightly more efficient at the cost of code readability.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t139" href="#t139">139</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t140" href="#t140">140</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t141" href="#t141">141</a></span><span class="t">    <span class="key">def</span> <span class="nam">integrate</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">Q</span><span class="op">=</span><span class="key">None</span><span class="op">,</span> <span class="nam">QI</span><span class="op">=</span><span class="key">None</span><span class="op">,</span> <span class="nam">QE</span><span class="op">=</span><span class="key">None</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t142" href="#t142">142</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t143" href="#t143">143</a></span><span class="t"><span class="str">        Integrates the right-hand side (here impl + expl)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t136" href="#t136">136</a></span><span class="t">        <span class="nam">res</span> <span class="op">=</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">-</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t137" href="#t137">137</a></span><span class="t">        <span class="key">for</span> <span class="nam">m</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="num">1</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">num_nodes</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t138" href="#t138">138</a></span><span class="t">            <span class="nam">res</span> <span class="op">+=</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">Qmat</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">,</span> <span class="nam">m</span><span class="op">]</span> <span class="op">*</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t139" href="#t139">139</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t140" href="#t140">140</a></span><span class="t">        <span class="key">if</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">residual_type</span><span class="op">[</span><span class="op">-</span><span class="num">3</span><span class="op">:</span><span class="op">]</span> <span class="op">==</span> <span class="str">'abs'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t141" href="#t141">141</a></span><span class="t">            <span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">residual</span> <span class="op">=</span> <span class="nam">abs</span><span class="op">(</span><span class="nam">res</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t142" href="#t142">142</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t143" href="#t143">143</a></span><span class="t">            <span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">residual</span> <span class="op">=</span> <span class="nam">abs</span><span class="op">(</span><span class="nam">res</span><span class="op">)</span> <span class="op">/</span> <span class="nam">abs</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t144" href="#t144">144</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t145" href="#t145">145</a></span><span class="t"><span class="str">        Args:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t146" href="#t146">146</a></span><span class="t"><span class="str">            Q (numpy.ndarray): Full quadrature rule</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t147" href="#t147">147</a></span><span class="t"><span class="str">            QI (numpy.ndarray): Implicit preconditioner</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t148" href="#t148">148</a></span><span class="t"><span class="str">            QE (numpy.ndarray): Explicit preconditioner</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t149" href="#t149">149</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t150" href="#t150">150</a></span><span class="t"><span class="str">        Returns:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t151" href="#t151">151</a></span><span class="t"><span class="str">            list of dtype_u: containing the integral as values</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t152" href="#t152">152</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t153" href="#t153">153</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t154" href="#t154">154</a></span><span class="t">        <span class="nam">Q</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">Qmat</span> <span class="key">if</span> <span class="nam">Q</span> <span class="key">is</span> <span class="key">None</span> <span class="key">else</span> <span class="nam">Q</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t155" href="#t155">155</a></span><span class="t">        <span class="nam">QI</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">zeros_like</span><span class="op">(</span><span class="nam">Q</span><span class="op">)</span> <span class="key">if</span> <span class="nam">QI</span> <span class="key">is</span> <span class="key">None</span> <span class="key">else</span> <span class="nam">QI</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t156" href="#t156">156</a></span><span class="t">        <span class="nam">QE</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">zeros_like</span><span class="op">(</span><span class="nam">Q</span><span class="op">)</span> <span class="key">if</span> <span class="nam">QE</span> <span class="key">is</span> <span class="key">None</span> <span class="key">else</span> <span class="nam">QE</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t157" href="#t157">157</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t158" href="#t158">158</a></span><span class="t">        <span class="com"># get current level and problem description</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t159" href="#t159">159</a></span><span class="t">        <span class="nam">L</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">level</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t160" href="#t160">160</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t161" href="#t161">161</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="op">[</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t162" href="#t162">162</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t163" href="#t163">163</a></span><span class="t">        <span class="com"># integrate RHS over all collocation nodes</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t164" href="#t164">164</a></span><span class="t">        <span class="key">for</span> <span class="nam">m</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="num">1</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">num_nodes</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t165" href="#t165">165</a></span><span class="t">            <span class="nam">me</span><span class="op">.</span><span class="nam">append</span><span class="op">(</span><span class="nam">L</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="op">(</span><span class="op">(</span><span class="nam">Q</span> <span class="op">-</span> <span class="nam">QI</span><span class="op">)</span><span class="op">[</span><span class="nam">m</span><span class="op">,</span> <span class="num">1</span><span class="op">]</span> <span class="op">*</span> <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">.</span><span class="nam">impl</span> <span class="op">+</span> <span class="op">(</span><span class="nam">Q</span> <span class="op">-</span> <span class="nam">QE</span><span class="op">)</span><span class="op">[</span><span class="nam">m</span><span class="op">,</span> <span class="num">1</span><span class="op">]</span> <span class="op">*</span> <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">.</span><span class="nam">expl</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t166" href="#t166">166</a></span><span class="t">            <span class="com"># new instance of dtype_u, initialize values with 0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t167" href="#t167">167</a></span><span class="t">            <span class="key">for</span> <span class="nam">j</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="num">2</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">num_nodes</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t168" href="#t168">168</a></span><span class="t">                <span class="nam">me</span><span class="op">[</span><span class="nam">m</span> <span class="op">-</span> <span class="num">1</span><span class="op">]</span> <span class="op">+=</span> <span class="nam">L</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="op">(</span><span class="op">(</span><span class="nam">Q</span> <span class="op">-</span> <span class="nam">QI</span><span class="op">)</span><span class="op">[</span><span class="nam">m</span><span class="op">,</span> <span class="nam">j</span><span class="op">]</span> <span class="op">*</span> <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">j</span><span class="op">]</span><span class="op">.</span><span class="nam">impl</span> <span class="op">+</span> <span class="op">(</span><span class="nam">Q</span> <span class="op">-</span> <span class="nam">QE</span><span class="op">)</span><span class="op">[</span><span class="nam">m</span><span class="op">,</span> <span class="nam">j</span><span class="op">]</span> <span class="op">*</span> <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">j</span><span class="op">]</span><span class="op">.</span><span class="nam">expl</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t145" href="#t145">145</a></span><span class="t">        <span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">updated</span> <span class="op">=</span> <span class="key">False</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t146" href="#t146">146</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t147" href="#t147">147</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t148" href="#t148">148</a></span><span class="t"><span class="key">class</span> <span class="nam">imex_1st_order_efficient</span><span class="op">(</span><span class="nam">efficient_sweeper</span><span class="op">,</span> <span class="nam">imex_1st_order</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t149" href="#t149">149</a></span><span class="t">    <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t150" href="#t150">150</a></span><span class="t"><span class="str">    Duplicate of `imex_1st_order` sweeper which is slightly more efficient at the cost of code readability.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t151" href="#t151">151</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t152" href="#t152">152</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t153" href="#t153">153</a></span><span class="t">    <span class="key">def</span> <span class="nam">integrate</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">Q</span><span class="op">=</span><span class="key">None</span><span class="op">,</span> <span class="nam">QI</span><span class="op">=</span><span class="key">None</span><span class="op">,</span> <span class="nam">QE</span><span class="op">=</span><span class="key">None</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t154" href="#t154">154</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t155" href="#t155">155</a></span><span class="t"><span class="str">        Integrates the right-hand side (here impl + expl)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t156" href="#t156">156</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t157" href="#t157">157</a></span><span class="t"><span class="str">        Args:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t158" href="#t158">158</a></span><span class="t"><span class="str">            Q (numpy.ndarray): Full quadrature rule</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t159" href="#t159">159</a></span><span class="t"><span class="str">            QI (numpy.ndarray): Implicit preconditioner</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t160" href="#t160">160</a></span><span class="t"><span class="str">            QE (numpy.ndarray): Explicit preconditioner</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t161" href="#t161">161</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t162" href="#t162">162</a></span><span class="t"><span class="str">        Returns:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t163" href="#t163">163</a></span><span class="t"><span class="str">            list of dtype_u: containing the integral as values</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t164" href="#t164">164</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t165" href="#t165">165</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t166" href="#t166">166</a></span><span class="t">        <span class="nam">Q</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">Qmat</span> <span class="key">if</span> <span class="nam">Q</span> <span class="key">is</span> <span class="key">None</span> <span class="key">else</span> <span class="nam">Q</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t167" href="#t167">167</a></span><span class="t">        <span class="nam">QI</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">zeros_like</span><span class="op">(</span><span class="nam">Q</span><span class="op">)</span> <span class="key">if</span> <span class="nam">QI</span> <span class="key">is</span> <span class="key">None</span> <span class="key">else</span> <span class="nam">QI</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t168" href="#t168">168</a></span><span class="t">        <span class="nam">QE</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">zeros_like</span><span class="op">(</span><span class="nam">Q</span><span class="op">)</span> <span class="key">if</span> <span class="nam">QE</span> <span class="key">is</span> <span class="key">None</span> <span class="key">else</span> <span class="nam">QE</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t169" href="#t169">169</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t170" href="#t170">170</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t171" href="#t171">171</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t172" href="#t172">172</a></span><span class="t">    <span class="key">def</span> <span class="nam">update_nodes</span><span class="op">(</span><span class="nam">self</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t173" href="#t173">173</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t174" href="#t174">174</a></span><span class="t"><span class="str">        Update the u- and f-values at the collocation nodes -> corresponds to a single sweep over all nodes</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t175" href="#t175">175</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t176" href="#t176">176</a></span><span class="t"><span class="str">        Returns:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t177" href="#t177">177</a></span><span class="t"><span class="str">            None</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t178" href="#t178">178</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t179" href="#t179">179</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t180" href="#t180">180</a></span><span class="t">        <span class="com"># get current level and problem description</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t181" href="#t181">181</a></span><span class="t">        <span class="nam">L</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">level</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t182" href="#t182">182</a></span><span class="t">        <span class="nam">P</span> <span class="op">=</span> <span class="nam">L</span><span class="op">.</span><span class="nam">prob</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t170" href="#t170">170</a></span><span class="t">        <span class="com"># get current level and problem description</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t171" href="#t171">171</a></span><span class="t">        <span class="nam">L</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">level</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t172" href="#t172">172</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t173" href="#t173">173</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="op">[</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t174" href="#t174">174</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t175" href="#t175">175</a></span><span class="t">        <span class="com"># integrate RHS over all collocation nodes</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t176" href="#t176">176</a></span><span class="t">        <span class="key">for</span> <span class="nam">m</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="num">1</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">num_nodes</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t177" href="#t177">177</a></span><span class="t">            <span class="nam">me</span><span class="op">.</span><span class="nam">append</span><span class="op">(</span><span class="nam">L</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="op">(</span><span class="op">(</span><span class="nam">Q</span> <span class="op">-</span> <span class="nam">QI</span><span class="op">)</span><span class="op">[</span><span class="nam">m</span><span class="op">,</span> <span class="num">1</span><span class="op">]</span> <span class="op">*</span> <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">.</span><span class="nam">impl</span> <span class="op">+</span> <span class="op">(</span><span class="nam">Q</span> <span class="op">-</span> <span class="nam">QE</span><span class="op">)</span><span class="op">[</span><span class="nam">m</span><span class="op">,</span> <span class="num">1</span><span class="op">]</span> <span class="op">*</span> <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">.</span><span class="nam">expl</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t178" href="#t178">178</a></span><span class="t">            <span class="com"># new instance of dtype_u, initialize values with 0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t179" href="#t179">179</a></span><span class="t">            <span class="key">for</span> <span class="nam">j</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="num">2</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">num_nodes</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t180" href="#t180">180</a></span><span class="t">                <span class="nam">me</span><span class="op">[</span><span class="nam">m</span> <span class="op">-</span> <span class="num">1</span><span class="op">]</span> <span class="op">+=</span> <span class="nam">L</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="op">(</span><span class="op">(</span><span class="nam">Q</span> <span class="op">-</span> <span class="nam">QI</span><span class="op">)</span><span class="op">[</span><span class="nam">m</span><span class="op">,</span> <span class="nam">j</span><span class="op">]</span> <span class="op">*</span> <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">j</span><span class="op">]</span><span class="op">.</span><span class="nam">impl</span> <span class="op">+</span> <span class="op">(</span><span class="nam">Q</span> <span class="op">-</span> <span class="nam">QE</span><span class="op">)</span><span class="op">[</span><span class="nam">m</span><span class="op">,</span> <span class="nam">j</span><span class="op">]</span> <span class="op">*</span> <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">j</span><span class="op">]</span><span class="op">.</span><span class="nam">expl</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t181" href="#t181">181</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t182" href="#t182">182</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t183" href="#t183">183</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t184" href="#t184">184</a></span><span class="t">        <span class="com"># only if the level has been touched before</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t185" href="#t185">185</a></span><span class="t">        <span class="key">assert</span> <span class="nam">L</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">unlocked</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t186" href="#t186">186</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t187" href="#t187">187</a></span><span class="t">        <span class="com"># get number of collocation nodes for easier access</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t188" href="#t188">188</a></span><span class="t">        <span class="nam">M</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">num_nodes</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t189" href="#t189">189</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t190" href="#t190">190</a></span><span class="t">        <span class="com"># gather all terms which are known already (e.g. from the previous iteration)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t191" href="#t191">191</a></span><span class="t">        <span class="com"># this corresponds to u0 + QF(u^k) - QIFI(u^k) - QEFE(u^k) + tau</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t192" href="#t192">192</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t193" href="#t193">193</a></span><span class="t">        <span class="com"># get QF(u^k)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t194" href="#t194">194</a></span><span class="t">        <span class="nam">integral</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">integrate</span><span class="op">(</span><span class="nam">Q</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">Qmat</span><span class="op">,</span> <span class="nam">QI</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">QI</span><span class="op">,</span> <span class="nam">QE</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">QE</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t195" href="#t195">195</a></span><span class="t">        <span class="key">for</span> <span class="nam">m</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">M</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t196" href="#t196">196</a></span><span class="t">            <span class="com"># add initial value</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t197" href="#t197">197</a></span><span class="t">            <span class="nam">integral</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span> <span class="op">+=</span> <span class="nam">L</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t198" href="#t198">198</a></span><span class="t">            <span class="com"># add tau if associated</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t199" href="#t199">199</a></span><span class="t">            <span class="key">if</span> <span class="nam">L</span><span class="op">.</span><span class="nam">tau</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span> <span class="key">is</span> <span class="key">not</span> <span class="key">None</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t200" href="#t200">200</a></span><span class="t">                <span class="nam">integral</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span> <span class="op">+=</span> <span class="nam">L</span><span class="op">.</span><span class="nam">tau</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t184" href="#t184">184</a></span><span class="t">    <span class="key">def</span> <span class="nam">update_nodes</span><span class="op">(</span><span class="nam">self</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t185" href="#t185">185</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t186" href="#t186">186</a></span><span class="t"><span class="str">        Update the u- and f-values at the collocation nodes -> corresponds to a single sweep over all nodes</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t187" href="#t187">187</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t188" href="#t188">188</a></span><span class="t"><span class="str">        Returns:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t189" href="#t189">189</a></span><span class="t"><span class="str">            None</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t190" href="#t190">190</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t191" href="#t191">191</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t192" href="#t192">192</a></span><span class="t">        <span class="com"># get current level and problem description</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t193" href="#t193">193</a></span><span class="t">        <span class="nam">L</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">level</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t194" href="#t194">194</a></span><span class="t">        <span class="nam">P</span> <span class="op">=</span> <span class="nam">L</span><span class="op">.</span><span class="nam">prob</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t195" href="#t195">195</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t196" href="#t196">196</a></span><span class="t">        <span class="com"># only if the level has been touched before</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t197" href="#t197">197</a></span><span class="t">        <span class="key">assert</span> <span class="nam">L</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">unlocked</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t198" href="#t198">198</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t199" href="#t199">199</a></span><span class="t">        <span class="com"># get number of collocation nodes for easier access</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t200" href="#t200">200</a></span><span class="t">        <span class="nam">M</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">num_nodes</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t201" href="#t201">201</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t202" href="#t202">202</a></span><span class="t">        <span class="com"># do the sweep</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t203" href="#t203">203</a></span><span class="t">        <span class="key">for</span> <span class="nam">m</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="num">0</span><span class="op">,</span> <span class="nam">M</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t204" href="#t204">204</a></span><span class="t">            <span class="com"># build rhs, consisting of the known values from above and new values from previous nodes (at k+1)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t205" href="#t205">205</a></span><span class="t">            <span class="nam">rhs</span> <span class="op">=</span> <span class="nam">P</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">integral</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t206" href="#t206">206</a></span><span class="t">            <span class="key">for</span> <span class="nam">j</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="num">1</span><span class="op">,</span> <span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t207" href="#t207">207</a></span><span class="t">                <span class="nam">rhs</span> <span class="op">+=</span> <span class="nam">L</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">QI</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">,</span> <span class="nam">j</span><span class="op">]</span> <span class="op">*</span> <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">j</span><span class="op">]</span><span class="op">.</span><span class="nam">impl</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">QE</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">,</span> <span class="nam">j</span><span class="op">]</span> <span class="op">*</span> <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">j</span><span class="op">]</span><span class="op">.</span><span class="nam">expl</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t208" href="#t208">208</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t209" href="#t209">209</a></span><span class="t">            <span class="com"># implicit solve with prefactor stemming from QI</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t210" href="#t210">210</a></span><span class="t">            <span class="nam">L</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">]</span> <span class="op">=</span> <span class="nam">P</span><span class="op">.</span><span class="nam">solve_system</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t211" href="#t211">211</a></span><span class="t">                <span class="nam">rhs</span><span class="op">,</span> <span class="nam">L</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">QI</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">,</span> <span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">]</span><span class="op">,</span> <span class="nam">L</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">]</span><span class="op">,</span> <span class="nam">L</span><span class="op">.</span><span class="nam">time</span> <span class="op">+</span> <span class="nam">L</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">nodes</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t212" href="#t212">212</a></span><span class="t">            <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t202" href="#t202">202</a></span><span class="t">        <span class="com"># gather all terms which are known already (e.g. from the previous iteration)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t203" href="#t203">203</a></span><span class="t">        <span class="com"># this corresponds to u0 + QF(u^k) - QIFI(u^k) - QEFE(u^k) + tau</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t204" href="#t204">204</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t205" href="#t205">205</a></span><span class="t">        <span class="com"># get QF(u^k)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t206" href="#t206">206</a></span><span class="t">        <span class="nam">integral</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">integrate</span><span class="op">(</span><span class="nam">Q</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">Qmat</span><span class="op">,</span> <span class="nam">QI</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">QI</span><span class="op">,</span> <span class="nam">QE</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">QE</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t207" href="#t207">207</a></span><span class="t">        <span class="key">for</span> <span class="nam">m</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">M</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t208" href="#t208">208</a></span><span class="t">            <span class="com"># add initial value</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t209" href="#t209">209</a></span><span class="t">            <span class="nam">integral</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span> <span class="op">+=</span> <span class="nam">L</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t210" href="#t210">210</a></span><span class="t">            <span class="com"># add tau if associated</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t211" href="#t211">211</a></span><span class="t">            <span class="key">if</span> <span class="nam">L</span><span class="op">.</span><span class="nam">tau</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span> <span class="key">is</span> <span class="key">not</span> <span class="key">None</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t212" href="#t212">212</a></span><span class="t">                <span class="nam">integral</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span> <span class="op">+=</span> <span class="nam">L</span><span class="op">.</span><span class="nam">tau</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t213" href="#t213">213</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t214" href="#t214">214</a></span><span class="t">            <span class="com"># update function values</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t215" href="#t215">215</a></span><span class="t">            <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">]</span> <span class="op">=</span> <span class="nam">P</span><span class="op">.</span><span class="nam">eval_f</span><span class="op">(</span><span class="nam">L</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">]</span><span class="op">,</span> <span class="nam">L</span><span class="op">.</span><span class="nam">time</span> <span class="op">+</span> <span class="nam">L</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">nodes</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t216" href="#t216">216</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t217" href="#t217">217</a></span><span class="t">        <span class="com"># indicate presence of new values at this level</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t218" href="#t218">218</a></span><span class="t">        <span class="nam">L</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">updated</span> <span class="op">=</span> <span class="key">True</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t219" href="#t219">219</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t220" href="#t220">220</a></span><span class="t">        <span class="key">return</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t214" href="#t214">214</a></span><span class="t">        <span class="com"># do the sweep</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t215" href="#t215">215</a></span><span class="t">        <span class="key">for</span> <span class="nam">m</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="num">0</span><span class="op">,</span> <span class="nam">M</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t216" href="#t216">216</a></span><span class="t">            <span class="com"># build rhs, consisting of the known values from above and new values from previous nodes (at k+1)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t217" href="#t217">217</a></span><span class="t">            <span class="nam">rhs</span> <span class="op">=</span> <span class="nam">P</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">integral</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t218" href="#t218">218</a></span><span class="t">            <span class="key">for</span> <span class="nam">j</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="num">1</span><span class="op">,</span> <span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t219" href="#t219">219</a></span><span class="t">                <span class="nam">rhs</span> <span class="op">+=</span> <span class="nam">L</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">QI</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">,</span> <span class="nam">j</span><span class="op">]</span> <span class="op">*</span> <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">j</span><span class="op">]</span><span class="op">.</span><span class="nam">impl</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">QE</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">,</span> <span class="nam">j</span><span class="op">]</span> <span class="op">*</span> <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">j</span><span class="op">]</span><span class="op">.</span><span class="nam">expl</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t220" href="#t220">220</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t221" href="#t221">221</a></span><span class="t">            <span class="com"># implicit solve with prefactor stemming from QI</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t222" href="#t222">222</a></span><span class="t">            <span class="nam">L</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">]</span> <span class="op">=</span> <span class="nam">P</span><span class="op">.</span><span class="nam">solve_system</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t223" href="#t223">223</a></span><span class="t">                <span class="nam">rhs</span><span class="op">,</span> <span class="nam">L</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">QI</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">,</span> <span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">]</span><span class="op">,</span> <span class="nam">L</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">]</span><span class="op">,</span> <span class="nam">L</span><span class="op">.</span><span class="nam">time</span> <span class="op">+</span> <span class="nam">L</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">nodes</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t224" href="#t224">224</a></span><span class="t">            <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t225" href="#t225">225</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t226" href="#t226">226</a></span><span class="t">            <span class="com"># update function values</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t227" href="#t227">227</a></span><span class="t">            <span class="nam">L</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">]</span> <span class="op">=</span> <span class="nam">P</span><span class="op">.</span><span class="nam">eval_f</span><span class="op">(</span><span class="nam">L</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">m</span> <span class="op">+</span> <span class="num">1</span><span class="op">]</span><span class="op">,</span> <span class="nam">L</span><span class="op">.</span><span class="nam">time</span> <span class="op">+</span> <span class="nam">L</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">nodes</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t228" href="#t228">228</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t229" href="#t229">229</a></span><span class="t">        <span class="com"># indicate presence of new values at this level</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t230" href="#t230">230</a></span><span class="t">        <span class="nam">L</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">updated</span> <span class="op">=</span> <span class="key">True</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t231" href="#t231">231</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t232" href="#t232">232</a></span><span class="t">        <span class="key">return</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t233" href="#t233">233</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t234" href="#t234">234</a></span><span class="t">    <span class="key">def</span> <span class="nam">compute_residual</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">stage</span><span class="op">=</span><span class="str">''</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t235" href="#t235">235</a></span><span class="t">        <span class="nam">lvl</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">level</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t236" href="#t236">236</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t237" href="#t237">237</a></span><span class="t">        <span class="key">if</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">residual_type</span><span class="op">[</span><span class="op">:</span><span class="num">4</span><span class="op">]</span> <span class="op">==</span> <span class="str">'full'</span> <span class="key">or</span> <span class="nam">stage</span> <span class="key">in</span> <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">skip_residual_computation</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t238" href="#t238">238</a></span><span class="t">            <span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">compute_residual</span><span class="op">(</span><span class="nam">stage</span><span class="op">=</span><span class="nam">stage</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t239" href="#t239">239</a></span><span class="t">            <span class="key">return</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t240" href="#t240">240</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t241" href="#t241">241</a></span><span class="t">        <span class="nam">res</span> <span class="op">=</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">-</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t242" href="#t242">242</a></span><span class="t">        <span class="key">for</span> <span class="nam">m</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="num">1</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">num_nodes</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t243" href="#t243">243</a></span><span class="t">            <span class="nam">res</span> <span class="op">+=</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">dt</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">Qmat</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">,</span> <span class="nam">m</span><span class="op">]</span> <span class="op">*</span> <span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span><span class="op">.</span><span class="nam">impl</span> <span class="op">+</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">m</span><span class="op">]</span><span class="op">.</span><span class="nam">expl</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t244" href="#t244">244</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t245" href="#t245">245</a></span><span class="t">        <span class="key">if</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">residual_type</span><span class="op">[</span><span class="op">-</span><span class="num">3</span><span class="op">:</span><span class="op">]</span> <span class="op">==</span> <span class="str">'abs'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t246" href="#t246">246</a></span><span class="t">            <span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">residual</span> <span class="op">=</span> <span class="nam">abs</span><span class="op">(</span><span class="nam">res</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t247" href="#t247">247</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t248" href="#t248">248</a></span><span class="t">            <span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">residual</span> <span class="op">=</span> <span class="nam">abs</span><span class="op">(</span><span class="nam">res</span><span class="op">)</span> <span class="op">/</span> <span class="nam">abs</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t249" href="#t249">249</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t250" href="#t250">250</a></span><span class="t">        <span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">updated</span> <span class="op">=</span> <span class="key">False</span>&nbsp;</span><span class="r"></span></p>
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 <footer>
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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--- a/coverage/d_60ee0c9d7735ef11_HookClass_acoustic_py.html
+++ b/coverage/d_60ee0c9d7735ef11_HookClass_acoustic_py.html
@@ -65,7 +65,7 @@ <h2>
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+            created at 2023-11-10 06:59 +0000
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         <aside class="hidden">
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+            created at 2023-11-10 06:59 +0000
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+++ b/coverage/d_60ee0c9d7735ef11_HookClass_boussinesq_py.html
@@ -65,7 +65,7 @@ <h2>
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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@@ -420,7 +420,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_8d0d803e4e125e5c_Sweeper_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
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 </footer>
diff --git a/coverage/d_8d0d803e4e125e5c_Sweeper_py.html b/coverage/d_8d0d803e4e125e5c_Sweeper_py.html
index b95029c293..767777e512 100644
--- a/coverage/d_8d0d803e4e125e5c_Sweeper_py.html
+++ b/coverage/d_8d0d803e4e125e5c_Sweeper_py.html
@@ -2,7 +2,7 @@
 <html>
 <head>
     <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
-    <title>Coverage for pySDC/core/Sweeper.py: 78%</title>
+    <title>Coverage for pySDC/core/Sweeper.py: 79%</title>
     <link rel="icon" sizes="32x32" href="favicon_32.png">
     <link rel="stylesheet" href="style.css" type="text/css">
     <script type="text/javascript" src="coverage_html.js" defer></script>
@@ -12,7 +12,7 @@
     <div class="content">
         <h1>
             <span class="text">Coverage for </span><b>pySDC/core/Sweeper.py</b>:
-            <span class="pc_cov">78%</span>
+            <span class="pc_cov">79%</span>
         </h1>
         <aside id="help_panel_wrapper">
             <input id="help_panel_state" type="checkbox">
@@ -55,8 +55,8 @@ <h1>
         </aside>
         <h2>
             <span class="text">215 statements &nbsp;</span>
-            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">167<span class="text"> run</span></button>
-            <button type="button" class="mis show_mis button_toggle_mis" value="mis" data-shortcut="m" title="Toggle lines missing">48<span class="text"> missing</span></button>
+            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">169<span class="text"> run</span></button>
+            <button type="button" class="mis show_mis button_toggle_mis" value="mis" data-shortcut="m" title="Toggle lines missing">46<span class="text"> missing</span></button>
             <button type="button" class="exc show_exc button_toggle_exc" value="exc" data-shortcut="x" title="Toggle lines excluded">10<span class="text"> excluded</span></button>
         </h2>
         <p class="text">
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_41564483689e14fd_plot_helper_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
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@@ -486,8 +486,8 @@ <h2>
     <p class="run"><span class="n"><a id="t404" href="#t404">404</a></span><span class="t">            <span class="nam">L</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">residual</span> <span class="op">=</span> <span class="nam">res_norm</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
     <p class="run"><span class="n"><a id="t405" href="#t405">405</a></span><span class="t">        <span class="key">elif</span> <span class="nam">L</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">residual_type</span> <span class="op">==</span> <span class="str">'full_rel'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
     <p class="run"><span class="n"><a id="t406" href="#t406">406</a></span><span class="t">            <span class="nam">L</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">residual</span> <span class="op">=</span> <span class="nam">max</span><span class="op">(</span><span class="nam">res_norm</span><span class="op">)</span> <span class="op">/</span> <span class="nam">abs</span><span class="op">(</span><span class="nam">L</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t407" href="#t407">407</a></span><span class="t">        <span class="key">elif</span> <span class="nam">L</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">residual_type</span> <span class="op">==</span> <span class="str">'last_rel'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t408" href="#t408">408</a></span><span class="t">            <span class="nam">L</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">residual</span> <span class="op">=</span> <span class="nam">res_norm</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span> <span class="op">/</span> <span class="nam">abs</span><span class="op">(</span><span class="nam">L</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t407" href="#t407">407</a></span><span class="t">        <span class="key">elif</span> <span class="nam">L</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">residual_type</span> <span class="op">==</span> <span class="str">'last_rel'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t408" href="#t408">408</a></span><span class="t">            <span class="nam">L</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">residual</span> <span class="op">=</span> <span class="nam">res_norm</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span> <span class="op">/</span> <span class="nam">abs</span><span class="op">(</span><span class="nam">L</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t409" href="#t409">409</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
     <p class="exc show_exc"><span class="n"><a id="t410" href="#t410">410</a></span><span class="t">            <span class="key">raise</span> <span class="nam">ParameterError</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t411" href="#t411">411</a></span><span class="t">                <span class="str">f'residual_type = {L.params.residual_type} not implemented, choose '</span>&nbsp;</span><span class="r"></span></p>
@@ -550,7 +550,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_41564483689e14fd_plot_helper_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
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diff --git a/coverage/d_91faa57f8583c837_AcousticAdvection_1D_FD_imex_py.html b/coverage/d_91faa57f8583c837_AcousticAdvection_1D_FD_imex_py.html
index d970f1647b..ce177cc272 100644
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+++ b/coverage/d_91faa57f8583c837_AcousticAdvection_1D_FD_imex_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_91faa57f8583c837_AdvectionDiffusionEquation_1D_FFT_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -309,7 +309,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_91faa57f8583c837_AdvectionDiffusionEquation_1D_FFT_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
     </div>
 </footer>
diff --git a/coverage/d_91faa57f8583c837_AdvectionDiffusionEquation_1D_FFT_py.html b/coverage/d_91faa57f8583c837_AdvectionDiffusionEquation_1D_FFT_py.html
index 3f2a815638..28fe29e72d 100644
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+++ b/coverage/d_91faa57f8583c837_AdvectionDiffusionEquation_1D_FFT_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_91faa57f8583c837_AdvectionEquation_ND_FD_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -327,7 +327,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_91faa57f8583c837_AdvectionEquation_ND_FD_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
     </div>
 </footer>
diff --git a/coverage/d_91faa57f8583c837_AdvectionEquation_ND_FD_py.html b/coverage/d_91faa57f8583c837_AdvectionEquation_ND_FD_py.html
index c356bb6155..b35d98c47e 100644
--- a/coverage/d_91faa57f8583c837_AdvectionEquation_ND_FD_py.html
+++ b/coverage/d_91faa57f8583c837_AdvectionEquation_ND_FD_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_91faa57f8583c837_AllenCahn_1D_FD_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -221,7 +221,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_91faa57f8583c837_AllenCahn_1D_FD_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
     </div>
 </footer>
diff --git a/coverage/d_91faa57f8583c837_AllenCahn_1D_FD_py.html b/coverage/d_91faa57f8583c837_AllenCahn_1D_FD_py.html
index b24d007bbc..a6ff46a966 100644
--- a/coverage/d_91faa57f8583c837_AllenCahn_1D_FD_py.html
+++ b/coverage/d_91faa57f8583c837_AllenCahn_1D_FD_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_91faa57f8583c837_AllenCahn_2D_FD_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -1018,7 +1018,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_91faa57f8583c837_AllenCahn_2D_FD_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
     </div>
 </footer>
diff --git a/coverage/d_91faa57f8583c837_AllenCahn_2D_FD_gpu_py.html b/coverage/d_91faa57f8583c837_AllenCahn_2D_FD_gpu_py.html
index 117fc82fc3..2caec9fa9d 100644
--- a/coverage/d_91faa57f8583c837_AllenCahn_2D_FD_gpu_py.html
+++ b/coverage/d_91faa57f8583c837_AllenCahn_2D_FD_gpu_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_91faa57f8583c837_AllenCahn_2D_FFT_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -828,7 +828,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_91faa57f8583c837_AllenCahn_2D_FFT_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
     </div>
 </footer>
diff --git a/coverage/d_91faa57f8583c837_AllenCahn_2D_FD_py.html b/coverage/d_91faa57f8583c837_AllenCahn_2D_FD_py.html
index 0cc9906916..6daa5da69b 100644
--- a/coverage/d_91faa57f8583c837_AllenCahn_2D_FD_py.html
+++ b/coverage/d_91faa57f8583c837_AllenCahn_2D_FD_py.html
@@ -2,7 +2,7 @@
 <html>
 <head>
     <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
-    <title>Coverage for pySDC/implementations/problem_classes/AllenCahn_2D_FD.py: 95%</title>
+    <title>Coverage for pySDC/implementations/problem_classes/AllenCahn_2D_FD.py: 92%</title>
     <link rel="icon" sizes="32x32" href="favicon_32.png">
     <link rel="stylesheet" href="style.css" type="text/css">
     <script type="text/javascript" src="coverage_html.js" defer></script>
@@ -12,7 +12,7 @@
     <div class="content">
         <h1>
             <span class="text">Coverage for </span><b>pySDC/implementations/problem_classes/AllenCahn_2D_FD.py</b>:
-            <span class="pc_cov">95%</span>
+            <span class="pc_cov">92%</span>
         </h1>
         <aside id="help_panel_wrapper">
             <input id="help_panel_state" type="checkbox">
@@ -54,9 +54,9 @@ <h1>
             </div>
         </aside>
         <h2>
-            <span class="text">191 statements &nbsp;</span>
-            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">182<span class="text"> run</span></button>
-            <button type="button" class="mis show_mis button_toggle_mis" value="mis" data-shortcut="m" title="Toggle lines missing">9<span class="text"> missing</span></button>
+            <span class="text">213 statements &nbsp;</span>
+            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">196<span class="text"> run</span></button>
+            <button type="button" class="mis show_mis button_toggle_mis" value="mis" data-shortcut="m" title="Toggle lines missing">17<span class="text"> missing</span></button>
             <button type="button" class="exc show_exc button_toggle_exc" value="exc" data-shortcut="x" title="Toggle lines excluded">8<span class="text"> excluded</span></button>
         </h2>
         <p class="text">
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_91faa57f8583c837_AllenCahn_2D_FD_gpu_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -85,7 +85,7 @@ <h2>
     <p class="run"><span class="n"><a id="t3" href="#t3">3</a></span><span class="t"><span class="key">from</span> <span class="nam">scipy</span><span class="op">.</span><span class="nam">sparse</span><span class="op">.</span><span class="nam">linalg</span> <span class="key">import</span> <span class="nam">cg</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t4" href="#t4">4</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
     <p class="run"><span class="n"><a id="t5" href="#t5">5</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">core</span><span class="op">.</span><span class="nam">Errors</span> <span class="key">import</span> <span class="nam">ParameterError</span><span class="op">,</span> <span class="nam">ProblemError</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t6" href="#t6">6</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">core</span><span class="op">.</span><span class="nam">Problem</span> <span class="key">import</span> <span class="nam">ptype</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t6" href="#t6">6</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">core</span><span class="op">.</span><span class="nam">Problem</span> <span class="key">import</span> <span class="nam">ptype</span><span class="op">,</span> <span class="nam">WorkCounter</span>&nbsp;</span><span class="r"></span></p>
     <p class="run"><span class="n"><a id="t7" href="#t7">7</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">helpers</span> <span class="key">import</span> <span class="nam">problem_helper</span>&nbsp;</span><span class="r"></span></p>
     <p class="run"><span class="n"><a id="t8" href="#t8">8</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">datatype_classes</span><span class="op">.</span><span class="nam">mesh</span> <span class="key">import</span> <span class="nam">mesh</span><span class="op">,</span> <span class="nam">imex_mesh</span><span class="op">,</span> <span class="nam">comp2_mesh</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t9" href="#t9">9</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
@@ -160,686 +160,739 @@ <h2>
     <p class="pln"><span class="n"><a id="t78" href="#t78">78</a></span><span class="t">        <span class="nam">newton_tol</span><span class="op">=</span><span class="num">1e-12</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t79" href="#t79">79</a></span><span class="t">        <span class="nam">lin_tol</span><span class="op">=</span><span class="num">1e-8</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t80" href="#t80">80</a></span><span class="t">        <span class="nam">lin_maxiter</span><span class="op">=</span><span class="num">100</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t81" href="#t81">81</a></span><span class="t">        <span class="nam">radius</span><span class="op">=</span><span class="num">0.25</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t82" href="#t82">82</a></span><span class="t">        <span class="nam">order</span><span class="op">=</span><span class="num">2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t83" href="#t83">83</a></span><span class="t">    <span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t84" href="#t84">84</a></span><span class="t">        <span class="str">"""Initialization routine"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t85" href="#t85">85</a></span><span class="t">        <span class="com"># we assert that nvars looks very particular here.. this will be necessary for coarsening in space later on</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t86" href="#t86">86</a></span><span class="t">        <span class="key">if</span> <span class="nam">len</span><span class="op">(</span><span class="nam">nvars</span><span class="op">)</span> <span class="op">!=</span> <span class="num">2</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t87" href="#t87">87</a></span><span class="t">            <span class="key">raise</span> <span class="nam">ProblemError</span><span class="op">(</span><span class="str">'this is a 2d example, got %s'</span> <span class="op">%</span> <span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t88" href="#t88">88</a></span><span class="t">        <span class="key">if</span> <span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">!=</span> <span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t89" href="#t89">89</a></span><span class="t">            <span class="key">raise</span> <span class="nam">ProblemError</span><span class="op">(</span><span class="str">'need a square domain, got %s'</span> <span class="op">%</span> <span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t90" href="#t90">90</a></span><span class="t">        <span class="key">if</span> <span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">%</span> <span class="num">2</span> <span class="op">!=</span> <span class="num">0</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t91" href="#t91">91</a></span><span class="t">            <span class="key">raise</span> <span class="nam">ProblemError</span><span class="op">(</span><span class="str">'the setup requires nvars = 2^p per dimension'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t92" href="#t92">92</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t93" href="#t93">93</a></span><span class="t">        <span class="com"># invoke super init, passing number of dofs, dtype_u and dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t94" href="#t94">94</a></span><span class="t">        <span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">__init__</span><span class="op">(</span><span class="op">(</span><span class="nam">nvars</span><span class="op">,</span> <span class="key">None</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">dtype</span><span class="op">(</span><span class="str">'float64'</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t95" href="#t95">95</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">_makeAttributeAndRegister</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t96" href="#t96">96</a></span><span class="t">            <span class="str">'nvars'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t97" href="#t97">97</a></span><span class="t">            <span class="str">'nu'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t98" href="#t98">98</a></span><span class="t">            <span class="str">'eps'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t99" href="#t99">99</a></span><span class="t">            <span class="str">'newton_maxiter'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t100" href="#t100">100</a></span><span class="t">            <span class="str">'newton_tol'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t101" href="#t101">101</a></span><span class="t">            <span class="str">'lin_tol'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t102" href="#t102">102</a></span><span class="t">            <span class="str">'lin_maxiter'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t103" href="#t103">103</a></span><span class="t">            <span class="str">'radius'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t104" href="#t104">104</a></span><span class="t">            <span class="str">'order'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t105" href="#t105">105</a></span><span class="t">            <span class="nam">localVars</span><span class="op">=</span><span class="nam">locals</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t106" href="#t106">106</a></span><span class="t">            <span class="nam">readOnly</span><span class="op">=</span><span class="key">True</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t107" href="#t107">107</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t108" href="#t108">108</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t109" href="#t109">109</a></span><span class="t">        <span class="com"># compute dx and get discretization matrix A</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t110" href="#t110">110</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">dx</span> <span class="op">=</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t111" href="#t111">111</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">,</span> <span class="nam">_</span> <span class="op">=</span> <span class="nam">problem_helper</span><span class="op">.</span><span class="nam">get_finite_difference_matrix</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t112" href="#t112">112</a></span><span class="t">            <span class="nam">derivative</span><span class="op">=</span><span class="num">2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t113" href="#t113">113</a></span><span class="t">            <span class="nam">order</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">order</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t114" href="#t114">114</a></span><span class="t">            <span class="nam">stencil_type</span><span class="op">=</span><span class="str">'center'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t115" href="#t115">115</a></span><span class="t">            <span class="nam">dx</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">dx</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t116" href="#t116">116</a></span><span class="t">            <span class="nam">size</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t117" href="#t117">117</a></span><span class="t">            <span class="nam">dim</span><span class="op">=</span><span class="num">2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t118" href="#t118">118</a></span><span class="t">            <span class="nam">bc</span><span class="op">=</span><span class="str">'periodic'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t119" href="#t119">119</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t120" href="#t120">120</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">xvalues</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">array</span><span class="op">(</span><span class="op">[</span><span class="nam">i</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dx</span> <span class="op">-</span> <span class="num">0.5</span> <span class="key">for</span> <span class="nam">i</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t121" href="#t121">121</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t122" href="#t122">122</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_itercount</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t123" href="#t123">123</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">lin_itercount</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t124" href="#t124">124</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_ncalls</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t125" href="#t125">125</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">lin_ncalls</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t126" href="#t126">126</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t127" href="#t127">127</a></span><span class="t">    <span class="op">@</span><span class="nam">staticmethod</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t128" href="#t128">128</a></span><span class="t">    <span class="key">def</span> <span class="nam">__get_A</span><span class="op">(</span><span class="nam">N</span><span class="op">,</span> <span class="nam">dx</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t129" href="#t129">129</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t130" href="#t130">130</a></span><span class="t"><span class="str">        Helper function to assemble FD matrix A in sparse format.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t131" href="#t131">131</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t132" href="#t132">132</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t133" href="#t133">133</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t134" href="#t134">134</a></span><span class="t"><span class="str">        N : list</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t135" href="#t135">135</a></span><span class="t"><span class="str">            Number of degrees of freedom.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t136" href="#t136">136</a></span><span class="t"><span class="str">        dx : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t137" href="#t137">137</a></span><span class="t"><span class="str">            Distance between two spatial nodes.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t138" href="#t138">138</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t139" href="#t139">139</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t140" href="#t140">140</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t141" href="#t141">141</a></span><span class="t"><span class="str">        A : scipy.sparse.csc_matrix</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t142" href="#t142">142</a></span><span class="t"><span class="str">            Matrix in CSC format.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t143" href="#t143">143</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t144" href="#t144">144</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t145" href="#t145">145</a></span><span class="t">        <span class="nam">stencil</span> <span class="op">=</span> <span class="op">[</span><span class="num">1</span><span class="op">,</span> <span class="op">-</span><span class="num">2</span><span class="op">,</span> <span class="num">1</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t146" href="#t146">146</a></span><span class="t">        <span class="nam">zero_pos</span> <span class="op">=</span> <span class="num">2</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t147" href="#t147">147</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t148" href="#t148">148</a></span><span class="t">        <span class="nam">dstencil</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">concatenate</span><span class="op">(</span><span class="op">(</span><span class="nam">stencil</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">delete</span><span class="op">(</span><span class="nam">stencil</span><span class="op">,</span> <span class="nam">zero_pos</span> <span class="op">-</span> <span class="num">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t149" href="#t149">149</a></span><span class="t">        <span class="nam">offsets</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">concatenate</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t150" href="#t150">150</a></span><span class="t">            <span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t151" href="#t151">151</a></span><span class="t">                <span class="op">[</span><span class="nam">N</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">-</span> <span class="nam">i</span> <span class="op">-</span> <span class="num">1</span> <span class="key">for</span> <span class="nam">i</span> <span class="key">in</span> <span class="nam">reversed</span><span class="op">(</span><span class="nam">range</span><span class="op">(</span><span class="nam">zero_pos</span> <span class="op">-</span> <span class="num">1</span><span class="op">)</span><span class="op">)</span><span class="op">]</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t152" href="#t152">152</a></span><span class="t">                <span class="op">[</span><span class="nam">i</span> <span class="op">-</span> <span class="nam">zero_pos</span> <span class="op">+</span> <span class="num">1</span> <span class="key">for</span> <span class="nam">i</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">zero_pos</span> <span class="op">-</span> <span class="num">1</span><span class="op">,</span> <span class="nam">len</span><span class="op">(</span><span class="nam">stencil</span><span class="op">)</span><span class="op">)</span><span class="op">]</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t153" href="#t153">153</a></span><span class="t">            <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t154" href="#t154">154</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t155" href="#t155">155</a></span><span class="t">        <span class="nam">doffsets</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">concatenate</span><span class="op">(</span><span class="op">(</span><span class="nam">offsets</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">delete</span><span class="op">(</span><span class="nam">offsets</span><span class="op">,</span> <span class="nam">zero_pos</span> <span class="op">-</span> <span class="num">1</span><span class="op">)</span> <span class="op">-</span> <span class="nam">N</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t156" href="#t156">156</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t157" href="#t157">157</a></span><span class="t">        <span class="nam">A</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">diags</span><span class="op">(</span><span class="nam">dstencil</span><span class="op">,</span> <span class="nam">doffsets</span><span class="op">,</span> <span class="nam">shape</span><span class="op">=</span><span class="op">(</span><span class="nam">N</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">,</span> <span class="nam">N</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">,</span> <span class="nam">format</span><span class="op">=</span><span class="str">'csc'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t158" href="#t158">158</a></span><span class="t">        <span class="nam">A</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">kron</span><span class="op">(</span><span class="nam">A</span><span class="op">,</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">N</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">kron</span><span class="op">(</span><span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">N</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span><span class="op">,</span> <span class="nam">A</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t159" href="#t159">159</a></span><span class="t">        <span class="nam">A</span> <span class="op">*=</span> <span class="num">1.0</span> <span class="op">/</span> <span class="op">(</span><span class="nam">dx</span><span class="op">**</span><span class="num">2</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t160" href="#t160">160</a></span><span class="t">        <span class="key">return</span> <span class="nam">A</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t161" href="#t161">161</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t162" href="#t162">162</a></span><span class="t">    <span class="com"># noinspection PyTypeChecker</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t163" href="#t163">163</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t164" href="#t164">164</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t165" href="#t165">165</a></span><span class="t"><span class="str">        Simple Newton solver.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t81" href="#t81">81</a></span><span class="t">        <span class="nam">inexact_linear_ratio</span><span class="op">=</span><span class="key">None</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t82" href="#t82">82</a></span><span class="t">        <span class="nam">radius</span><span class="op">=</span><span class="num">0.25</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t83" href="#t83">83</a></span><span class="t">        <span class="nam">order</span><span class="op">=</span><span class="num">2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t84" href="#t84">84</a></span><span class="t">    <span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t85" href="#t85">85</a></span><span class="t">        <span class="str">"""Initialization routine"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t86" href="#t86">86</a></span><span class="t">        <span class="com"># we assert that nvars looks very particular here.. this will be necessary for coarsening in space later on</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t87" href="#t87">87</a></span><span class="t">        <span class="key">if</span> <span class="nam">len</span><span class="op">(</span><span class="nam">nvars</span><span class="op">)</span> <span class="op">!=</span> <span class="num">2</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t88" href="#t88">88</a></span><span class="t">            <span class="key">raise</span> <span class="nam">ProblemError</span><span class="op">(</span><span class="str">'this is a 2d example, got %s'</span> <span class="op">%</span> <span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t89" href="#t89">89</a></span><span class="t">        <span class="key">if</span> <span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">!=</span> <span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t90" href="#t90">90</a></span><span class="t">            <span class="key">raise</span> <span class="nam">ProblemError</span><span class="op">(</span><span class="str">'need a square domain, got %s'</span> <span class="op">%</span> <span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t91" href="#t91">91</a></span><span class="t">        <span class="key">if</span> <span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">%</span> <span class="num">2</span> <span class="op">!=</span> <span class="num">0</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t92" href="#t92">92</a></span><span class="t">            <span class="key">raise</span> <span class="nam">ProblemError</span><span class="op">(</span><span class="str">'the setup requires nvars = 2^p per dimension'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t93" href="#t93">93</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t94" href="#t94">94</a></span><span class="t">        <span class="com"># invoke super init, passing number of dofs, dtype_u and dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t95" href="#t95">95</a></span><span class="t">        <span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">__init__</span><span class="op">(</span><span class="op">(</span><span class="nam">nvars</span><span class="op">,</span> <span class="key">None</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">dtype</span><span class="op">(</span><span class="str">'float64'</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t96" href="#t96">96</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">_makeAttributeAndRegister</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t97" href="#t97">97</a></span><span class="t">            <span class="str">'nvars'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t98" href="#t98">98</a></span><span class="t">            <span class="str">'nu'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t99" href="#t99">99</a></span><span class="t">            <span class="str">'eps'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t100" href="#t100">100</a></span><span class="t">            <span class="str">'radius'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t101" href="#t101">101</a></span><span class="t">            <span class="str">'order'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t102" href="#t102">102</a></span><span class="t">            <span class="nam">localVars</span><span class="op">=</span><span class="nam">locals</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t103" href="#t103">103</a></span><span class="t">            <span class="nam">readOnly</span><span class="op">=</span><span class="key">True</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t104" href="#t104">104</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t105" href="#t105">105</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">_makeAttributeAndRegister</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t106" href="#t106">106</a></span><span class="t">            <span class="str">'newton_maxiter'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t107" href="#t107">107</a></span><span class="t">            <span class="str">'newton_tol'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t108" href="#t108">108</a></span><span class="t">            <span class="str">'lin_tol'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t109" href="#t109">109</a></span><span class="t">            <span class="str">'lin_maxiter'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t110" href="#t110">110</a></span><span class="t">            <span class="str">'inexact_linear_ratio'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t111" href="#t111">111</a></span><span class="t">            <span class="nam">localVars</span><span class="op">=</span><span class="nam">locals</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t112" href="#t112">112</a></span><span class="t">            <span class="nam">readOnly</span><span class="op">=</span><span class="key">False</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t113" href="#t113">113</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t114" href="#t114">114</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t115" href="#t115">115</a></span><span class="t">        <span class="com"># compute dx and get discretization matrix A</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t116" href="#t116">116</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">dx</span> <span class="op">=</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t117" href="#t117">117</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">,</span> <span class="nam">_</span> <span class="op">=</span> <span class="nam">problem_helper</span><span class="op">.</span><span class="nam">get_finite_difference_matrix</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t118" href="#t118">118</a></span><span class="t">            <span class="nam">derivative</span><span class="op">=</span><span class="num">2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t119" href="#t119">119</a></span><span class="t">            <span class="nam">order</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">order</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t120" href="#t120">120</a></span><span class="t">            <span class="nam">stencil_type</span><span class="op">=</span><span class="str">'center'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t121" href="#t121">121</a></span><span class="t">            <span class="nam">dx</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">dx</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t122" href="#t122">122</a></span><span class="t">            <span class="nam">size</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t123" href="#t123">123</a></span><span class="t">            <span class="nam">dim</span><span class="op">=</span><span class="num">2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t124" href="#t124">124</a></span><span class="t">            <span class="nam">bc</span><span class="op">=</span><span class="str">'periodic'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t125" href="#t125">125</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t126" href="#t126">126</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">xvalues</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">array</span><span class="op">(</span><span class="op">[</span><span class="nam">i</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dx</span> <span class="op">-</span> <span class="num">0.5</span> <span class="key">for</span> <span class="nam">i</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t127" href="#t127">127</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t128" href="#t128">128</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_itercount</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t129" href="#t129">129</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">lin_itercount</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t130" href="#t130">130</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_ncalls</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t131" href="#t131">131</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">lin_ncalls</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t132" href="#t132">132</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t133" href="#t133">133</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'newton'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">WorkCounter</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t134" href="#t134">134</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'rhs'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">WorkCounter</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t135" href="#t135">135</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'linear'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">WorkCounter</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t136" href="#t136">136</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t137" href="#t137">137</a></span><span class="t">    <span class="op">@</span><span class="nam">staticmethod</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t138" href="#t138">138</a></span><span class="t">    <span class="key">def</span> <span class="nam">__get_A</span><span class="op">(</span><span class="nam">N</span><span class="op">,</span> <span class="nam">dx</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t139" href="#t139">139</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t140" href="#t140">140</a></span><span class="t"><span class="str">        Helper function to assemble FD matrix A in sparse format.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t141" href="#t141">141</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t142" href="#t142">142</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t143" href="#t143">143</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t144" href="#t144">144</a></span><span class="t"><span class="str">        N : list</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t145" href="#t145">145</a></span><span class="t"><span class="str">            Number of degrees of freedom.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t146" href="#t146">146</a></span><span class="t"><span class="str">        dx : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t147" href="#t147">147</a></span><span class="t"><span class="str">            Distance between two spatial nodes.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t148" href="#t148">148</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t149" href="#t149">149</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t150" href="#t150">150</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t151" href="#t151">151</a></span><span class="t"><span class="str">        A : scipy.sparse.csc_matrix</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t152" href="#t152">152</a></span><span class="t"><span class="str">            Matrix in CSC format.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t153" href="#t153">153</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t154" href="#t154">154</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t155" href="#t155">155</a></span><span class="t">        <span class="nam">stencil</span> <span class="op">=</span> <span class="op">[</span><span class="num">1</span><span class="op">,</span> <span class="op">-</span><span class="num">2</span><span class="op">,</span> <span class="num">1</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t156" href="#t156">156</a></span><span class="t">        <span class="nam">zero_pos</span> <span class="op">=</span> <span class="num">2</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t157" href="#t157">157</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t158" href="#t158">158</a></span><span class="t">        <span class="nam">dstencil</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">concatenate</span><span class="op">(</span><span class="op">(</span><span class="nam">stencil</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">delete</span><span class="op">(</span><span class="nam">stencil</span><span class="op">,</span> <span class="nam">zero_pos</span> <span class="op">-</span> <span class="num">1</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t159" href="#t159">159</a></span><span class="t">        <span class="nam">offsets</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">concatenate</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t160" href="#t160">160</a></span><span class="t">            <span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t161" href="#t161">161</a></span><span class="t">                <span class="op">[</span><span class="nam">N</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">-</span> <span class="nam">i</span> <span class="op">-</span> <span class="num">1</span> <span class="key">for</span> <span class="nam">i</span> <span class="key">in</span> <span class="nam">reversed</span><span class="op">(</span><span class="nam">range</span><span class="op">(</span><span class="nam">zero_pos</span> <span class="op">-</span> <span class="num">1</span><span class="op">)</span><span class="op">)</span><span class="op">]</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t162" href="#t162">162</a></span><span class="t">                <span class="op">[</span><span class="nam">i</span> <span class="op">-</span> <span class="nam">zero_pos</span> <span class="op">+</span> <span class="num">1</span> <span class="key">for</span> <span class="nam">i</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">zero_pos</span> <span class="op">-</span> <span class="num">1</span><span class="op">,</span> <span class="nam">len</span><span class="op">(</span><span class="nam">stencil</span><span class="op">)</span><span class="op">)</span><span class="op">]</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t163" href="#t163">163</a></span><span class="t">            <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t164" href="#t164">164</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t165" href="#t165">165</a></span><span class="t">        <span class="nam">doffsets</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">concatenate</span><span class="op">(</span><span class="op">(</span><span class="nam">offsets</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">delete</span><span class="op">(</span><span class="nam">offsets</span><span class="op">,</span> <span class="nam">zero_pos</span> <span class="op">-</span> <span class="num">1</span><span class="op">)</span> <span class="op">-</span> <span class="nam">N</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t166" href="#t166">166</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t167" href="#t167">167</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t168" href="#t168">168</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t169" href="#t169">169</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t170" href="#t170">170</a></span><span class="t"><span class="str">            Right-hand side for the nonlinear system</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t171" href="#t171">171</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t172" href="#t172">172</a></span><span class="t"><span class="str">            Abbrev. for the node-to-node stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t173" href="#t173">173</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t174" href="#t174">174</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t175" href="#t175">175</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t176" href="#t176">176</a></span><span class="t"><span class="str">            Current time (required here for the BC).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t177" href="#t177">177</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t178" href="#t178">178</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t179" href="#t179">179</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t180" href="#t180">180</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t181" href="#t181">181</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t182" href="#t182">182</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t183" href="#t183">183</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t184" href="#t184">184</a></span><span class="t">        <span class="nam">u</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">u0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t185" href="#t185">185</a></span><span class="t">        <span class="nam">z</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t186" href="#t186">186</a></span><span class="t">        <span class="nam">nu</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nu</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t187" href="#t187">187</a></span><span class="t">        <span class="nam">eps2</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t188" href="#t188">188</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t189" href="#t189">189</a></span><span class="t">        <span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t190" href="#t190">190</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t191" href="#t191">191</a></span><span class="t">        <span class="com"># start newton iteration</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t192" href="#t192">192</a></span><span class="t">        <span class="nam">n</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t193" href="#t193">193</a></span><span class="t">        <span class="nam">res</span> <span class="op">=</span> <span class="num">99</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t194" href="#t194">194</a></span><span class="t">        <span class="key">while</span> <span class="nam">n</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_maxiter</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t195" href="#t195">195</a></span><span class="t">            <span class="com"># form the function g with g(u) = 0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t196" href="#t196">196</a></span><span class="t">            <span class="nam">g</span> <span class="op">=</span> <span class="nam">u</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span> <span class="op">+</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">u</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="nam">u</span><span class="op">**</span><span class="nam">nu</span><span class="op">)</span><span class="op">)</span> <span class="op">-</span> <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t197" href="#t197">197</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t198" href="#t198">198</a></span><span class="t">            <span class="com"># if g is close to 0, then we are done</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t199" href="#t199">199</a></span><span class="t">            <span class="nam">res</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">linalg</span><span class="op">.</span><span class="nam">norm</span><span class="op">(</span><span class="nam">g</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">inf</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t167" href="#t167">167</a></span><span class="t">        <span class="nam">A</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">diags</span><span class="op">(</span><span class="nam">dstencil</span><span class="op">,</span> <span class="nam">doffsets</span><span class="op">,</span> <span class="nam">shape</span><span class="op">=</span><span class="op">(</span><span class="nam">N</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">,</span> <span class="nam">N</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">,</span> <span class="nam">format</span><span class="op">=</span><span class="str">'csc'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t168" href="#t168">168</a></span><span class="t">        <span class="nam">A</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">kron</span><span class="op">(</span><span class="nam">A</span><span class="op">,</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">N</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">kron</span><span class="op">(</span><span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">N</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span><span class="op">,</span> <span class="nam">A</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t169" href="#t169">169</a></span><span class="t">        <span class="nam">A</span> <span class="op">*=</span> <span class="num">1.0</span> <span class="op">/</span> <span class="op">(</span><span class="nam">dx</span><span class="op">**</span><span class="num">2</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t170" href="#t170">170</a></span><span class="t">        <span class="key">return</span> <span class="nam">A</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t171" href="#t171">171</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t172" href="#t172">172</a></span><span class="t">    <span class="com"># noinspection PyTypeChecker</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t173" href="#t173">173</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t174" href="#t174">174</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t175" href="#t175">175</a></span><span class="t"><span class="str">        Simple Newton solver.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t176" href="#t176">176</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t177" href="#t177">177</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t178" href="#t178">178</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t179" href="#t179">179</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t180" href="#t180">180</a></span><span class="t"><span class="str">            Right-hand side for the nonlinear system</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t181" href="#t181">181</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t182" href="#t182">182</a></span><span class="t"><span class="str">            Abbrev. for the node-to-node stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t183" href="#t183">183</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t184" href="#t184">184</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t185" href="#t185">185</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t186" href="#t186">186</a></span><span class="t"><span class="str">            Current time (required here for the BC).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t187" href="#t187">187</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t188" href="#t188">188</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t189" href="#t189">189</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t190" href="#t190">190</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t191" href="#t191">191</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t192" href="#t192">192</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t193" href="#t193">193</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t194" href="#t194">194</a></span><span class="t">        <span class="nam">u</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">u0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t195" href="#t195">195</a></span><span class="t">        <span class="nam">z</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t196" href="#t196">196</a></span><span class="t">        <span class="nam">nu</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nu</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t197" href="#t197">197</a></span><span class="t">        <span class="nam">eps2</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t198" href="#t198">198</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t199" href="#t199">199</a></span><span class="t">        <span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t200" href="#t200">200</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t201" href="#t201">201</a></span><span class="t">            <span class="key">if</span> <span class="nam">res</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_tol</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t202" href="#t202">202</a></span><span class="t">                <span class="key">break</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t203" href="#t203">203</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t204" href="#t204">204</a></span><span class="t">            <span class="com"># assemble dg</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t205" href="#t205">205</a></span><span class="t">            <span class="nam">dg</span> <span class="op">=</span> <span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span> <span class="op">+</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">diags</span><span class="op">(</span><span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="op">(</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span> <span class="op">*</span> <span class="nam">u</span><span class="op">**</span><span class="nam">nu</span><span class="op">)</span><span class="op">,</span> <span class="nam">offsets</span><span class="op">=</span><span class="num">0</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t206" href="#t206">206</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t207" href="#t207">207</a></span><span class="t">            <span class="com"># newton update: u1 = u0 - g/dg</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t208" href="#t208">208</a></span><span class="t">            <span class="com"># u -= spsolve(dg, g)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t209" href="#t209">209</a></span><span class="t">            <span class="nam">u</span> <span class="op">-=</span> <span class="nam">cg</span><span class="op">(</span><span class="nam">dg</span><span class="op">,</span> <span class="nam">g</span><span class="op">,</span> <span class="nam">x0</span><span class="op">=</span><span class="nam">z</span><span class="op">,</span> <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_tol</span><span class="op">,</span> <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">)</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t210" href="#t210">210</a></span><span class="t">            <span class="com"># increase iteration count</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t211" href="#t211">211</a></span><span class="t">            <span class="nam">n</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t212" href="#t212">212</a></span><span class="t">            <span class="com"># print(n, res)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t213" href="#t213">213</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t214" href="#t214">214</a></span><span class="t">        <span class="com"># if n == self.newton_maxiter:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t215" href="#t215">215</a></span><span class="t">        <span class="com">#     raise ProblemError('Newton did not converge after %i iterations, error is %s' % (n, res))</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t216" href="#t216">216</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t217" href="#t217">217</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t218" href="#t218">218</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t219" href="#t219">219</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t220" href="#t220">220</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_ncalls</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t221" href="#t221">221</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_itercount</span> <span class="op">+=</span> <span class="nam">n</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t222" href="#t222">222</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t223" href="#t223">223</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t224" href="#t224">224</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t225" href="#t225">225</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t226" href="#t226">226</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t227" href="#t227">227</a></span><span class="t"><span class="str">        Routine to evaluate the right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t228" href="#t228">228</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t229" href="#t229">229</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t230" href="#t230">230</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t231" href="#t231">231</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t232" href="#t232">232</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t233" href="#t233">233</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t234" href="#t234">234</a></span><span class="t"><span class="str">            Current time of the numerical solution is computed (not used here).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t235" href="#t235">235</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t236" href="#t236">236</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t237" href="#t237">237</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t238" href="#t238">238</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t239" href="#t239">239</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t240" href="#t240">240</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t241" href="#t241">241</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t242" href="#t242">242</a></span><span class="t">        <span class="nam">v</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t243" href="#t243">243</a></span><span class="t">        <span class="nam">f</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">v</span><span class="op">)</span> <span class="op">+</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="nam">v</span><span class="op">**</span><span class="nam">self</span><span class="op">.</span><span class="nam">nu</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t244" href="#t244">244</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t245" href="#t245">245</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t201" href="#t201">201</a></span><span class="t">        <span class="com"># start newton iteration</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t202" href="#t202">202</a></span><span class="t">        <span class="nam">n</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t203" href="#t203">203</a></span><span class="t">        <span class="nam">res</span> <span class="op">=</span> <span class="num">99</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t204" href="#t204">204</a></span><span class="t">        <span class="key">while</span> <span class="nam">n</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_maxiter</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t205" href="#t205">205</a></span><span class="t">            <span class="com"># form the function g with g(u) = 0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t206" href="#t206">206</a></span><span class="t">            <span class="nam">g</span> <span class="op">=</span> <span class="nam">u</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span> <span class="op">+</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">u</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="nam">u</span><span class="op">**</span><span class="nam">nu</span><span class="op">)</span><span class="op">)</span> <span class="op">-</span> <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t207" href="#t207">207</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t208" href="#t208">208</a></span><span class="t">            <span class="com"># if g is close to 0, then we are done</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t209" href="#t209">209</a></span><span class="t">            <span class="nam">res</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">linalg</span><span class="op">.</span><span class="nam">norm</span><span class="op">(</span><span class="nam">g</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">inf</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t210" href="#t210">210</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t211" href="#t211">211</a></span><span class="t">            <span class="com"># do inexactness in the linear solver</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t212" href="#t212">212</a></span><span class="t">            <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">inexact_linear_ratio</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t213" href="#t213">213</a></span><span class="t">                <span class="nam">self</span><span class="op">.</span><span class="nam">lin_tol</span> <span class="op">=</span> <span class="nam">res</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">inexact_linear_ratio</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t214" href="#t214">214</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t215" href="#t215">215</a></span><span class="t">            <span class="key">if</span> <span class="nam">res</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_tol</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t216" href="#t216">216</a></span><span class="t">                <span class="key">break</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t217" href="#t217">217</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t218" href="#t218">218</a></span><span class="t">            <span class="com"># assemble dg</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t219" href="#t219">219</a></span><span class="t">            <span class="nam">dg</span> <span class="op">=</span> <span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span> <span class="op">+</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">diags</span><span class="op">(</span><span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="op">(</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span> <span class="op">*</span> <span class="nam">u</span><span class="op">**</span><span class="nam">nu</span><span class="op">)</span><span class="op">,</span> <span class="nam">offsets</span><span class="op">=</span><span class="num">0</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t220" href="#t220">220</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t221" href="#t221">221</a></span><span class="t">            <span class="com"># newton update: u1 = u0 - g/dg</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t222" href="#t222">222</a></span><span class="t">            <span class="com"># u -= spsolve(dg, g)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t223" href="#t223">223</a></span><span class="t">            <span class="nam">u</span> <span class="op">-=</span> <span class="nam">cg</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t224" href="#t224">224</a></span><span class="t">                <span class="nam">dg</span><span class="op">,</span> <span class="nam">g</span><span class="op">,</span> <span class="nam">x0</span><span class="op">=</span><span class="nam">z</span><span class="op">,</span> <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_tol</span><span class="op">,</span> <span class="nam">maxiter</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_maxiter</span><span class="op">,</span> <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">,</span> <span class="nam">callback</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'linear'</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t225" href="#t225">225</a></span><span class="t">            <span class="op">)</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t226" href="#t226">226</a></span><span class="t">            <span class="com"># increase iteration count</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t227" href="#t227">227</a></span><span class="t">            <span class="nam">n</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t228" href="#t228">228</a></span><span class="t">            <span class="com"># print(n, res)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t229" href="#t229">229</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t230" href="#t230">230</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'newton'</span><span class="op">]</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t231" href="#t231">231</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t232" href="#t232">232</a></span><span class="t">        <span class="com"># if n == self.newton_maxiter:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t233" href="#t233">233</a></span><span class="t">        <span class="com">#     raise ProblemError('Newton did not converge after %i iterations, error is %s' % (n, res))</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t234" href="#t234">234</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t235" href="#t235">235</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t236" href="#t236">236</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t237" href="#t237">237</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t238" href="#t238">238</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_ncalls</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t239" href="#t239">239</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_itercount</span> <span class="op">+=</span> <span class="nam">n</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t240" href="#t240">240</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t241" href="#t241">241</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t242" href="#t242">242</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t243" href="#t243">243</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t244" href="#t244">244</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t245" href="#t245">245</a></span><span class="t"><span class="str">        Routine to evaluate the right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t246" href="#t246">246</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t247" href="#t247">247</a></span><span class="t">    <span class="key">def</span> <span class="nam">u_exact</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t248" href="#t248">248</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t249" href="#t249">249</a></span><span class="t"><span class="str">        Routine to compute the exact solution at time :math:`t`.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t250" href="#t250">250</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t251" href="#t251">251</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t252" href="#t252">252</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t253" href="#t253">253</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t254" href="#t254">254</a></span><span class="t"><span class="str">            Time of the exact solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t255" href="#t255">255</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t256" href="#t256">256</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t257" href="#t257">257</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t258" href="#t258">258</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t259" href="#t259">259</a></span><span class="t"><span class="str">            The exact solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t260" href="#t260">260</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t261" href="#t261">261</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t262" href="#t262">262</a></span><span class="t">        <span class="key">assert</span> <span class="nam">t</span> <span class="op">==</span> <span class="num">0</span><span class="op">,</span> <span class="str">'ERROR: u_exact only valid for t=0'</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t263" href="#t263">263</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t264" href="#t264">264</a></span><span class="t">        <span class="key">for</span> <span class="nam">i</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t265" href="#t265">265</a></span><span class="t">            <span class="key">for</span> <span class="nam">j</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t266" href="#t266">266</a></span><span class="t">                <span class="nam">r2</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">xvalues</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span> <span class="op">**</span> <span class="num">2</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">xvalues</span><span class="op">[</span><span class="nam">j</span><span class="op">]</span> <span class="op">**</span> <span class="num">2</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t267" href="#t267">267</a></span><span class="t">                <span class="nam">me</span><span class="op">[</span><span class="nam">i</span><span class="op">,</span> <span class="nam">j</span><span class="op">]</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">tanh</span><span class="op">(</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">radius</span> <span class="op">-</span> <span class="nam">np</span><span class="op">.</span><span class="nam">sqrt</span><span class="op">(</span><span class="nam">r2</span><span class="op">)</span><span class="op">)</span> <span class="op">/</span> <span class="op">(</span><span class="nam">np</span><span class="op">.</span><span class="nam">sqrt</span><span class="op">(</span><span class="num">2</span><span class="op">)</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t268" href="#t268">268</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t269" href="#t269">269</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t270" href="#t270">270</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t271" href="#t271">271</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t272" href="#t272">272</a></span><span class="t"><span class="com"># noinspection PyUnusedLocal</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t273" href="#t273">273</a></span><span class="t"><span class="key">class</span> <span class="nam">allencahn_semiimplicit</span><span class="op">(</span><span class="nam">allencahn_fullyimplicit</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t274" href="#t274">274</a></span><span class="t">    <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t275" href="#t275">275</a></span><span class="t"><span class="str">    This class implements the two-dimensional Allen-Cahn equation with periodic boundary conditions :math:`u \in [-1, 1]^2`</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t276" href="#t276">276</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t277" href="#t277">277</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t278" href="#t278">278</a></span><span class="t"><span class="str">        \frac{\partial u}{\partial t} = \Delta u + \frac{1}{\varepsilon^2} u (1 - u^\nu)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t279" href="#t279">279</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t280" href="#t280">280</a></span><span class="t"><span class="str">    for constant parameter :math:`\nu`. Initial condition are circles of the form</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t281" href="#t281">281</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t282" href="#t282">282</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t283" href="#t283">283</a></span><span class="t"><span class="str">        u({\bf x}, 0) = \tanh\left(\frac{r - \sqrt{x_i^2 + y_j^2}}{\sqrt{2}\varepsilon}\right)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t284" href="#t284">284</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t285" href="#t285">285</a></span><span class="t"><span class="str">    for :math:`i, j=0,..,N-1`, where :math:`N` is the number of spatial grid points. For time-stepping, the problem is</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t286" href="#t286">286</a></span><span class="t"><span class="str">    treated in a *semi-implicit* way, i.e., the linear system containing the Laplacian is solved by the conjugate gradients</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t287" href="#t287">287</a></span><span class="t"><span class="str">    method, and the system containing the rest of the right-hand side is only evaluated at each time.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t288" href="#t288">288</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t289" href="#t289">289</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t290" href="#t290">290</a></span><span class="t">    <span class="nam">dtype_f</span> <span class="op">=</span> <span class="nam">imex_mesh</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t291" href="#t291">291</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t292" href="#t292">292</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t293" href="#t293">293</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t294" href="#t294">294</a></span><span class="t"><span class="str">        Routine to evaluate the right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t247" href="#t247">247</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t248" href="#t248">248</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t249" href="#t249">249</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t250" href="#t250">250</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t251" href="#t251">251</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t252" href="#t252">252</a></span><span class="t"><span class="str">            Current time of the numerical solution is computed (not used here).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t253" href="#t253">253</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t254" href="#t254">254</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t255" href="#t255">255</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t256" href="#t256">256</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t257" href="#t257">257</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t258" href="#t258">258</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t259" href="#t259">259</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t260" href="#t260">260</a></span><span class="t">        <span class="nam">v</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t261" href="#t261">261</a></span><span class="t">        <span class="nam">f</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">v</span><span class="op">)</span> <span class="op">+</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="nam">v</span><span class="op">**</span><span class="nam">self</span><span class="op">.</span><span class="nam">nu</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t262" href="#t262">262</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t263" href="#t263">263</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'rhs'</span><span class="op">]</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t264" href="#t264">264</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t265" href="#t265">265</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t266" href="#t266">266</a></span><span class="t">    <span class="key">def</span> <span class="nam">u_exact</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">=</span><span class="key">None</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">=</span><span class="key">None</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t267" href="#t267">267</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t268" href="#t268">268</a></span><span class="t"><span class="str">        Routine to compute the exact solution at time :math:`t`.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t269" href="#t269">269</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t270" href="#t270">270</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t271" href="#t271">271</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t272" href="#t272">272</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t273" href="#t273">273</a></span><span class="t"><span class="str">            Time of the exact solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t274" href="#t274">274</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t275" href="#t275">275</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t276" href="#t276">276</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t277" href="#t277">277</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t278" href="#t278">278</a></span><span class="t"><span class="str">            The exact solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t279" href="#t279">279</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t280" href="#t280">280</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t281" href="#t281">281</a></span><span class="t">        <span class="key">if</span> <span class="nam">t</span> <span class="op">></span> <span class="num">0</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t282" href="#t282">282</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t283" href="#t283">283</a></span><span class="t">            <span class="key">def</span> <span class="nam">eval_rhs</span><span class="op">(</span><span class="nam">t</span><span class="op">,</span> <span class="nam">u</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t284" href="#t284">284</a></span><span class="t">                <span class="key">return</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eval_f</span><span class="op">(</span><span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t285" href="#t285">285</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t286" href="#t286">286</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">generate_scipy_reference_solution</span><span class="op">(</span><span class="nam">eval_rhs</span><span class="op">,</span> <span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t287" href="#t287">287</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t288" href="#t288">288</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t289" href="#t289">289</a></span><span class="t">            <span class="key">for</span> <span class="nam">i</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t290" href="#t290">290</a></span><span class="t">                <span class="key">for</span> <span class="nam">j</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t291" href="#t291">291</a></span><span class="t">                    <span class="nam">r2</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">xvalues</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span> <span class="op">**</span> <span class="num">2</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">xvalues</span><span class="op">[</span><span class="nam">j</span><span class="op">]</span> <span class="op">**</span> <span class="num">2</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t292" href="#t292">292</a></span><span class="t">                    <span class="nam">me</span><span class="op">[</span><span class="nam">i</span><span class="op">,</span> <span class="nam">j</span><span class="op">]</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">tanh</span><span class="op">(</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">radius</span> <span class="op">-</span> <span class="nam">np</span><span class="op">.</span><span class="nam">sqrt</span><span class="op">(</span><span class="nam">r2</span><span class="op">)</span><span class="op">)</span> <span class="op">/</span> <span class="op">(</span><span class="nam">np</span><span class="op">.</span><span class="nam">sqrt</span><span class="op">(</span><span class="num">2</span><span class="op">)</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t293" href="#t293">293</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t294" href="#t294">294</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t295" href="#t295">295</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t296" href="#t296">296</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t297" href="#t297">297</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t298" href="#t298">298</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t299" href="#t299">299</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t300" href="#t300">300</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t301" href="#t301">301</a></span><span class="t"><span class="str">            Current time of the numerical solution is computed (not used here).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t302" href="#t302">302</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t303" href="#t303">303</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t304" href="#t304">304</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t305" href="#t305">305</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t306" href="#t306">306</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t307" href="#t307">307</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t308" href="#t308">308</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t309" href="#t309">309</a></span><span class="t">        <span class="nam">v</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t310" href="#t310">310</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">impl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">v</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t311" href="#t311">311</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">expl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="nam">v</span><span class="op">**</span><span class="nam">self</span><span class="op">.</span><span class="nam">nu</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t312" href="#t312">312</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t313" href="#t313">313</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t296" href="#t296">296</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t297" href="#t297">297</a></span><span class="t"><span class="com"># noinspection PyUnusedLocal</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t298" href="#t298">298</a></span><span class="t"><span class="key">class</span> <span class="nam">allencahn_semiimplicit</span><span class="op">(</span><span class="nam">allencahn_fullyimplicit</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t299" href="#t299">299</a></span><span class="t">    <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t300" href="#t300">300</a></span><span class="t"><span class="str">    This class implements the two-dimensional Allen-Cahn equation with periodic boundary conditions :math:`u \in [-1, 1]^2`</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t301" href="#t301">301</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t302" href="#t302">302</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t303" href="#t303">303</a></span><span class="t"><span class="str">        \frac{\partial u}{\partial t} = \Delta u + \frac{1}{\varepsilon^2} u (1 - u^\nu)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t304" href="#t304">304</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t305" href="#t305">305</a></span><span class="t"><span class="str">    for constant parameter :math:`\nu`. Initial condition are circles of the form</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t306" href="#t306">306</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t307" href="#t307">307</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t308" href="#t308">308</a></span><span class="t"><span class="str">        u({\bf x}, 0) = \tanh\left(\frac{r - \sqrt{x_i^2 + y_j^2}}{\sqrt{2}\varepsilon}\right)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t309" href="#t309">309</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t310" href="#t310">310</a></span><span class="t"><span class="str">    for :math:`i, j=0,..,N-1`, where :math:`N` is the number of spatial grid points. For time-stepping, the problem is</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t311" href="#t311">311</a></span><span class="t"><span class="str">    treated in a *semi-implicit* way, i.e., the linear system containing the Laplacian is solved by the conjugate gradients</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t312" href="#t312">312</a></span><span class="t"><span class="str">    method, and the system containing the rest of the right-hand side is only evaluated at each time.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t313" href="#t313">313</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t314" href="#t314">314</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t315" href="#t315">315</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t316" href="#t316">316</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t317" href="#t317">317</a></span><span class="t"><span class="str">        Simple linear solver for :math:`(I-factor\cdot A)\vec{u}=\vec{rhs}`.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t318" href="#t318">318</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t319" href="#t319">319</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t320" href="#t320">320</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t321" href="#t321">321</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t322" href="#t322">322</a></span><span class="t"><span class="str">            Right-hand side for the linear system.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t323" href="#t323">323</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t324" href="#t324">324</a></span><span class="t"><span class="str">            Abbrev. for the local stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t325" href="#t325">325</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t326" href="#t326">326</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t327" href="#t327">327</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t328" href="#t328">328</a></span><span class="t"><span class="str">            Current time (e.g. for time-dependent BCs).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t329" href="#t329">329</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t330" href="#t330">330</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t331" href="#t331">331</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t332" href="#t332">332</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t333" href="#t333">333</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t334" href="#t334">334</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t335" href="#t335">335</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t336" href="#t336">336</a></span><span class="t">        <span class="key">class</span> <span class="nam">context</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t337" href="#t337">337</a></span><span class="t">            <span class="nam">num_iter</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t338" href="#t338">338</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t339" href="#t339">339</a></span><span class="t">        <span class="key">def</span> <span class="nam">callback</span><span class="op">(</span><span class="nam">xk</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t340" href="#t340">340</a></span><span class="t">            <span class="nam">context</span><span class="op">.</span><span class="nam">num_iter</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t341" href="#t341">341</a></span><span class="t">            <span class="key">return</span> <span class="nam">context</span><span class="op">.</span><span class="nam">num_iter</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t342" href="#t342">342</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t343" href="#t343">343</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t315" href="#t315">315</a></span><span class="t">    <span class="nam">dtype_f</span> <span class="op">=</span> <span class="nam">imex_mesh</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t316" href="#t316">316</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t317" href="#t317">317</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t318" href="#t318">318</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t319" href="#t319">319</a></span><span class="t"><span class="str">        Routine to evaluate the right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t320" href="#t320">320</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t321" href="#t321">321</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t322" href="#t322">322</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t323" href="#t323">323</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t324" href="#t324">324</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t325" href="#t325">325</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t326" href="#t326">326</a></span><span class="t"><span class="str">            Current time of the numerical solution is computed (not used here).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t327" href="#t327">327</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t328" href="#t328">328</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t329" href="#t329">329</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t330" href="#t330">330</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t331" href="#t331">331</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t332" href="#t332">332</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t333" href="#t333">333</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t334" href="#t334">334</a></span><span class="t">        <span class="nam">v</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t335" href="#t335">335</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">impl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">v</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t336" href="#t336">336</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">expl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="nam">v</span><span class="op">**</span><span class="nam">self</span><span class="op">.</span><span class="nam">nu</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t337" href="#t337">337</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t338" href="#t338">338</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'rhs'</span><span class="op">]</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t339" href="#t339">339</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t340" href="#t340">340</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t341" href="#t341">341</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t342" href="#t342">342</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t343" href="#t343">343</a></span><span class="t"><span class="str">        Simple linear solver for :math:`(I-factor\cdot A)\vec{u}=\vec{rhs}`.</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t344" href="#t344">344</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t345" href="#t345">345</a></span><span class="t">        <span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t346" href="#t346">346</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t347" href="#t347">347</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">cg</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t348" href="#t348">348</a></span><span class="t">            <span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t349" href="#t349">349</a></span><span class="t">            <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t350" href="#t350">350</a></span><span class="t">            <span class="nam">x0</span><span class="op">=</span><span class="nam">u0</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t351" href="#t351">351</a></span><span class="t">            <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_tol</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t352" href="#t352">352</a></span><span class="t">            <span class="nam">maxiter</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_maxiter</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t353" href="#t353">353</a></span><span class="t">            <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t354" href="#t354">354</a></span><span class="t">            <span class="nam">callback</span><span class="op">=</span><span class="nam">callback</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t355" href="#t355">355</a></span><span class="t">        <span class="op">)</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t356" href="#t356">356</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t357" href="#t357">357</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">lin_ncalls</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t358" href="#t358">358</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">lin_itercount</span> <span class="op">+=</span> <span class="nam">context</span><span class="op">.</span><span class="nam">num_iter</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t359" href="#t359">359</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t360" href="#t360">360</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t345" href="#t345">345</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t346" href="#t346">346</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t347" href="#t347">347</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t348" href="#t348">348</a></span><span class="t"><span class="str">            Right-hand side for the linear system.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t349" href="#t349">349</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t350" href="#t350">350</a></span><span class="t"><span class="str">            Abbrev. for the local stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t351" href="#t351">351</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t352" href="#t352">352</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t353" href="#t353">353</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t354" href="#t354">354</a></span><span class="t"><span class="str">            Current time (e.g. for time-dependent BCs).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t355" href="#t355">355</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t356" href="#t356">356</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t357" href="#t357">357</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t358" href="#t358">358</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t359" href="#t359">359</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t360" href="#t360">360</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t361" href="#t361">361</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t362" href="#t362">362</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t363" href="#t363">363</a></span><span class="t"><span class="com"># noinspection PyUnusedLocal</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t364" href="#t364">364</a></span><span class="t"><span class="key">class</span> <span class="nam">allencahn_semiimplicit_v2</span><span class="op">(</span><span class="nam">allencahn_fullyimplicit</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t365" href="#t365">365</a></span><span class="t">    <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t366" href="#t366">366</a></span><span class="t"><span class="str">    This class implements the two-dimensional Allen-Cahn (AC) equation with periodic boundary conditions :math:`u \in [-1, 1]^2`</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t367" href="#t367">367</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t368" href="#t368">368</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t369" href="#t369">369</a></span><span class="t"><span class="str">        \frac{\partial u}{\partial t} = \Delta u + \frac{1}{\varepsilon^2} u (1 - u^\nu)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t370" href="#t370">370</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t371" href="#t371">371</a></span><span class="t"><span class="str">    for constant parameter :math:`\nu`. Initial condition are circles of the form</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t372" href="#t372">372</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t373" href="#t373">373</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t374" href="#t374">374</a></span><span class="t"><span class="str">        u({\bf x}, 0) = \tanh\left(\frac{r - \sqrt{x_i^2 + y_j^2}}{\sqrt{2}\varepsilon}\right)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t375" href="#t375">375</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t376" href="#t376">376</a></span><span class="t"><span class="str">    for :math:`i, j=0,..,N-1`, where :math:`N` is the number of spatial grid points. For time-stepping, a special AC-splitting</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t377" href="#t377">377</a></span><span class="t"><span class="str">    is used to get a *semi-implicit* treatment of the problem: The term :math:`\Delta u - \frac{1}{\varepsilon^2} u^{\nu + 1}`</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t378" href="#t378">378</a></span><span class="t"><span class="str">    is handled implicitly and the nonlinear system including this part will be solved by Newton. :math:`\frac{1}{\varepsilon^2} u`</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t379" href="#t379">379</a></span><span class="t"><span class="str">    is only evaluated at each time.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t380" href="#t380">380</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t381" href="#t381">381</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t382" href="#t382">382</a></span><span class="t">    <span class="nam">dtype_f</span> <span class="op">=</span> <span class="nam">imex_mesh</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t362" href="#t362">362</a></span><span class="t">        <span class="key">class</span> <span class="nam">context</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t363" href="#t363">363</a></span><span class="t">            <span class="nam">num_iter</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t364" href="#t364">364</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t365" href="#t365">365</a></span><span class="t">        <span class="key">def</span> <span class="nam">callback</span><span class="op">(</span><span class="nam">xk</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t366" href="#t366">366</a></span><span class="t">            <span class="nam">context</span><span class="op">.</span><span class="nam">num_iter</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t367" href="#t367">367</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'linear'</span><span class="op">]</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t368" href="#t368">368</a></span><span class="t">            <span class="key">return</span> <span class="nam">context</span><span class="op">.</span><span class="nam">num_iter</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t369" href="#t369">369</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t370" href="#t370">370</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t371" href="#t371">371</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t372" href="#t372">372</a></span><span class="t">        <span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t373" href="#t373">373</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t374" href="#t374">374</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">cg</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t375" href="#t375">375</a></span><span class="t">            <span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t376" href="#t376">376</a></span><span class="t">            <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t377" href="#t377">377</a></span><span class="t">            <span class="nam">x0</span><span class="op">=</span><span class="nam">u0</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t378" href="#t378">378</a></span><span class="t">            <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_tol</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t379" href="#t379">379</a></span><span class="t">            <span class="nam">maxiter</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_maxiter</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t380" href="#t380">380</a></span><span class="t">            <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t381" href="#t381">381</a></span><span class="t">            <span class="nam">callback</span><span class="op">=</span><span class="nam">callback</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t382" href="#t382">382</a></span><span class="t">        <span class="op">)</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t383" href="#t383">383</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t384" href="#t384">384</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t385" href="#t385">385</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t386" href="#t386">386</a></span><span class="t"><span class="str">        Routine to evaluate the right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t387" href="#t387">387</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t388" href="#t388">388</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t389" href="#t389">389</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t390" href="#t390">390</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t391" href="#t391">391</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t392" href="#t392">392</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t393" href="#t393">393</a></span><span class="t"><span class="str">            Current time of the numerical solution is computed.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t394" href="#t394">394</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t395" href="#t395">395</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t396" href="#t396">396</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t397" href="#t397">397</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t398" href="#t398">398</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t399" href="#t399">399</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t400" href="#t400">400</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t401" href="#t401">401</a></span><span class="t">        <span class="nam">v</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t402" href="#t402">402</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">impl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">v</span><span class="op">)</span> <span class="op">-</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span> <span class="op">**</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t403" href="#t403">403</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">expl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t404" href="#t404">404</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t405" href="#t405">405</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t406" href="#t406">406</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t407" href="#t407">407</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t408" href="#t408">408</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t409" href="#t409">409</a></span><span class="t"><span class="str">        Simple Newton solver.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t410" href="#t410">410</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t411" href="#t411">411</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t412" href="#t412">412</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t413" href="#t413">413</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t414" href="#t414">414</a></span><span class="t"><span class="str">            Right-hand side for the nonlinear system.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t415" href="#t415">415</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t416" href="#t416">416</a></span><span class="t"><span class="str">            Abbrev. for the node-to-node stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t417" href="#t417">417</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t418" href="#t418">418</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t419" href="#t419">419</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t420" href="#t420">420</a></span><span class="t"><span class="str">            Current time (required here for the BC).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t421" href="#t421">421</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t422" href="#t422">422</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t423" href="#t423">423</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t424" href="#t424">424</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t425" href="#t425">425</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t426" href="#t426">426</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t427" href="#t427">427</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t428" href="#t428">428</a></span><span class="t">        <span class="nam">u</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">u0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t429" href="#t429">429</a></span><span class="t">        <span class="nam">z</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t430" href="#t430">430</a></span><span class="t">        <span class="nam">nu</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nu</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t431" href="#t431">431</a></span><span class="t">        <span class="nam">eps2</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t432" href="#t432">432</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t433" href="#t433">433</a></span><span class="t">        <span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t384" href="#t384">384</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">lin_ncalls</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t385" href="#t385">385</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">lin_itercount</span> <span class="op">+=</span> <span class="nam">context</span><span class="op">.</span><span class="nam">num_iter</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t386" href="#t386">386</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t387" href="#t387">387</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t388" href="#t388">388</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t389" href="#t389">389</a></span><span class="t">    <span class="key">def</span> <span class="nam">u_exact</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">=</span><span class="key">None</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">=</span><span class="key">None</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t390" href="#t390">390</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t391" href="#t391">391</a></span><span class="t"><span class="str">        Routine to compute the exact solution at time t.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t392" href="#t392">392</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t393" href="#t393">393</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t394" href="#t394">394</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t395" href="#t395">395</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t396" href="#t396">396</a></span><span class="t"><span class="str">            Time of the exact solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t397" href="#t397">397</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t398" href="#t398">398</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t399" href="#t399">399</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t400" href="#t400">400</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t401" href="#t401">401</a></span><span class="t"><span class="str">            The exact solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t402" href="#t402">402</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t403" href="#t403">403</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t404" href="#t404">404</a></span><span class="t">        <span class="key">if</span> <span class="nam">t</span> <span class="op">></span> <span class="num">0</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t405" href="#t405">405</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t406" href="#t406">406</a></span><span class="t">            <span class="key">def</span> <span class="nam">eval_rhs</span><span class="op">(</span><span class="nam">t</span><span class="op">,</span> <span class="nam">u</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t407" href="#t407">407</a></span><span class="t">                <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eval_f</span><span class="op">(</span><span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t408" href="#t408">408</a></span><span class="t">                <span class="key">return</span> <span class="op">(</span><span class="nam">f</span><span class="op">.</span><span class="nam">impl</span> <span class="op">+</span> <span class="nam">f</span><span class="op">.</span><span class="nam">expl</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t409" href="#t409">409</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t410" href="#t410">410</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">generate_scipy_reference_solution</span><span class="op">(</span><span class="nam">eval_rhs</span><span class="op">,</span> <span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t411" href="#t411">411</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t412" href="#t412">412</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">u_exact</span><span class="op">(</span><span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t413" href="#t413">413</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t414" href="#t414">414</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t415" href="#t415">415</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t416" href="#t416">416</a></span><span class="t"><span class="com"># noinspection PyUnusedLocal</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t417" href="#t417">417</a></span><span class="t"><span class="key">class</span> <span class="nam">allencahn_semiimplicit_v2</span><span class="op">(</span><span class="nam">allencahn_fullyimplicit</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t418" href="#t418">418</a></span><span class="t">    <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t419" href="#t419">419</a></span><span class="t"><span class="str">    This class implements the two-dimensional Allen-Cahn (AC) equation with periodic boundary conditions :math:`u \in [-1, 1]^2`</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t420" href="#t420">420</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t421" href="#t421">421</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t422" href="#t422">422</a></span><span class="t"><span class="str">        \frac{\partial u}{\partial t} = \Delta u + \frac{1}{\varepsilon^2} u (1 - u^\nu)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t423" href="#t423">423</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t424" href="#t424">424</a></span><span class="t"><span class="str">    for constant parameter :math:`\nu`. Initial condition are circles of the form</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t425" href="#t425">425</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t426" href="#t426">426</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t427" href="#t427">427</a></span><span class="t"><span class="str">        u({\bf x}, 0) = \tanh\left(\frac{r - \sqrt{x_i^2 + y_j^2}}{\sqrt{2}\varepsilon}\right)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t428" href="#t428">428</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t429" href="#t429">429</a></span><span class="t"><span class="str">    for :math:`i, j=0,..,N-1`, where :math:`N` is the number of spatial grid points. For time-stepping, a special AC-splitting</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t430" href="#t430">430</a></span><span class="t"><span class="str">    is used to get a *semi-implicit* treatment of the problem: The term :math:`\Delta u - \frac{1}{\varepsilon^2} u^{\nu + 1}`</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t431" href="#t431">431</a></span><span class="t"><span class="str">    is handled implicitly and the nonlinear system including this part will be solved by Newton. :math:`\frac{1}{\varepsilon^2} u`</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t432" href="#t432">432</a></span><span class="t"><span class="str">    is only evaluated at each time.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t433" href="#t433">433</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t434" href="#t434">434</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t435" href="#t435">435</a></span><span class="t">        <span class="com"># start newton iteration</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t436" href="#t436">436</a></span><span class="t">        <span class="nam">n</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t437" href="#t437">437</a></span><span class="t">        <span class="nam">res</span> <span class="op">=</span> <span class="num">99</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t438" href="#t438">438</a></span><span class="t">        <span class="key">while</span> <span class="nam">n</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_maxiter</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t439" href="#t439">439</a></span><span class="t">            <span class="com"># form the function g with g(u) = 0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t440" href="#t440">440</a></span><span class="t">            <span class="nam">g</span> <span class="op">=</span> <span class="nam">u</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span> <span class="op">-</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">u</span> <span class="op">**</span> <span class="op">(</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">)</span> <span class="op">-</span> <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t441" href="#t441">441</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t442" href="#t442">442</a></span><span class="t">            <span class="com"># if g is close to 0, then we are done</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t443" href="#t443">443</a></span><span class="t">            <span class="com"># res = np.linalg.norm(g, np.inf)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t444" href="#t444">444</a></span><span class="t">            <span class="nam">res</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">linalg</span><span class="op">.</span><span class="nam">norm</span><span class="op">(</span><span class="nam">g</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">inf</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t445" href="#t445">445</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t446" href="#t446">446</a></span><span class="t">            <span class="key">if</span> <span class="nam">res</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_tol</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t447" href="#t447">447</a></span><span class="t">                <span class="key">break</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t448" href="#t448">448</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t449" href="#t449">449</a></span><span class="t">            <span class="com"># assemble dg</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t450" href="#t450">450</a></span><span class="t">            <span class="nam">dg</span> <span class="op">=</span> <span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span> <span class="op">-</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">diags</span><span class="op">(</span><span class="op">(</span><span class="op">(</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span> <span class="op">*</span> <span class="nam">u</span><span class="op">**</span><span class="nam">nu</span><span class="op">)</span><span class="op">,</span> <span class="nam">offsets</span><span class="op">=</span><span class="num">0</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t451" href="#t451">451</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t452" href="#t452">452</a></span><span class="t">            <span class="com"># newton update: u1 = u0 - g/dg</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t453" href="#t453">453</a></span><span class="t">            <span class="com"># u -= spsolve(dg, g)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t454" href="#t454">454</a></span><span class="t">            <span class="nam">u</span> <span class="op">-=</span> <span class="nam">cg</span><span class="op">(</span><span class="nam">dg</span><span class="op">,</span> <span class="nam">g</span><span class="op">,</span> <span class="nam">x0</span><span class="op">=</span><span class="nam">z</span><span class="op">,</span> <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_tol</span><span class="op">,</span> <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">)</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t455" href="#t455">455</a></span><span class="t">            <span class="com"># increase iteration count</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t456" href="#t456">456</a></span><span class="t">            <span class="nam">n</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t457" href="#t457">457</a></span><span class="t">            <span class="com"># print(n, res)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t458" href="#t458">458</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t459" href="#t459">459</a></span><span class="t">        <span class="com"># if n == self.newton_maxiter:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t460" href="#t460">460</a></span><span class="t">        <span class="com">#     raise ProblemError('Newton did not converge after %i iterations, error is %s' % (n, res))</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t461" href="#t461">461</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t462" href="#t462">462</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t463" href="#t463">463</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t464" href="#t464">464</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t465" href="#t465">465</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_ncalls</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t466" href="#t466">466</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_itercount</span> <span class="op">+=</span> <span class="nam">n</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t467" href="#t467">467</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t468" href="#t468">468</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t469" href="#t469">469</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t470" href="#t470">470</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t471" href="#t471">471</a></span><span class="t"><span class="com"># noinspection PyUnusedLocal</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t472" href="#t472">472</a></span><span class="t"><span class="key">class</span> <span class="nam">allencahn_multiimplicit</span><span class="op">(</span><span class="nam">allencahn_fullyimplicit</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t473" href="#t473">473</a></span><span class="t">    <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t474" href="#t474">474</a></span><span class="t"><span class="str">    Example implementing the two-dimensional Allen-Cahn equation with periodic boundary conditions :math:`u \in [-1, 1]^2`</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t475" href="#t475">475</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t476" href="#t476">476</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t477" href="#t477">477</a></span><span class="t"><span class="str">        \frac{\partial u}{\partial t} = \Delta u + \frac{1}{\varepsilon^2} u (1 - u^\nu)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t478" href="#t478">478</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t479" href="#t479">479</a></span><span class="t"><span class="str">    for constant parameter :math:`\nu`. Initial condition are circles of the form</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t435" href="#t435">435</a></span><span class="t">    <span class="nam">dtype_f</span> <span class="op">=</span> <span class="nam">imex_mesh</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t436" href="#t436">436</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t437" href="#t437">437</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t438" href="#t438">438</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t439" href="#t439">439</a></span><span class="t"><span class="str">        Routine to evaluate the right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t440" href="#t440">440</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t441" href="#t441">441</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t442" href="#t442">442</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t443" href="#t443">443</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t444" href="#t444">444</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t445" href="#t445">445</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t446" href="#t446">446</a></span><span class="t"><span class="str">            Current time of the numerical solution is computed.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t447" href="#t447">447</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t448" href="#t448">448</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t449" href="#t449">449</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t450" href="#t450">450</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t451" href="#t451">451</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t452" href="#t452">452</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t453" href="#t453">453</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t454" href="#t454">454</a></span><span class="t">        <span class="nam">v</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t455" href="#t455">455</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">impl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">v</span><span class="op">)</span> <span class="op">-</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span> <span class="op">**</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t456" href="#t456">456</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">expl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t457" href="#t457">457</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t458" href="#t458">458</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t459" href="#t459">459</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t460" href="#t460">460</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t461" href="#t461">461</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t462" href="#t462">462</a></span><span class="t"><span class="str">        Simple Newton solver.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t463" href="#t463">463</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t464" href="#t464">464</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t465" href="#t465">465</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t466" href="#t466">466</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t467" href="#t467">467</a></span><span class="t"><span class="str">            Right-hand side for the nonlinear system.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t468" href="#t468">468</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t469" href="#t469">469</a></span><span class="t"><span class="str">            Abbrev. for the node-to-node stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t470" href="#t470">470</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t471" href="#t471">471</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t472" href="#t472">472</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t473" href="#t473">473</a></span><span class="t"><span class="str">            Current time (required here for the BC).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t474" href="#t474">474</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t475" href="#t475">475</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t476" href="#t476">476</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t477" href="#t477">477</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t478" href="#t478">478</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t479" href="#t479">479</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t480" href="#t480">480</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t481" href="#t481">481</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t482" href="#t482">482</a></span><span class="t"><span class="str">        u({\bf x}, 0) = \tanh\left(\frac{r - \sqrt{x_i^2 + y_j^2}}{\sqrt{2}\varepsilon}\right)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t483" href="#t483">483</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t484" href="#t484">484</a></span><span class="t"><span class="str">    for :math:`i, j=0,..,N-1`, where :math:`N` is the number of spatial grid points. For time-stepping, the problem is</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t485" href="#t485">485</a></span><span class="t"><span class="str">    treated in *multi-implicit* fashion, i.e., the linear system containing the Laplacian is solved by the conjugate gradients</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t486" href="#t486">486</a></span><span class="t"><span class="str">    method, and the system containing the rest of the right-hand side will be solved by Newton's method.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t487" href="#t487">487</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t488" href="#t488">488</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t489" href="#t489">489</a></span><span class="t">    <span class="nam">dtype_f</span> <span class="op">=</span> <span class="nam">comp2_mesh</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t490" href="#t490">490</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t491" href="#t491">491</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t492" href="#t492">492</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t493" href="#t493">493</a></span><span class="t"><span class="str">        Routine to evaluate the right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t481" href="#t481">481</a></span><span class="t">        <span class="nam">u</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">u0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t482" href="#t482">482</a></span><span class="t">        <span class="nam">z</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t483" href="#t483">483</a></span><span class="t">        <span class="nam">nu</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nu</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t484" href="#t484">484</a></span><span class="t">        <span class="nam">eps2</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t485" href="#t485">485</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t486" href="#t486">486</a></span><span class="t">        <span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t487" href="#t487">487</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t488" href="#t488">488</a></span><span class="t">        <span class="com"># start newton iteration</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t489" href="#t489">489</a></span><span class="t">        <span class="nam">n</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t490" href="#t490">490</a></span><span class="t">        <span class="nam">res</span> <span class="op">=</span> <span class="num">99</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t491" href="#t491">491</a></span><span class="t">        <span class="key">while</span> <span class="nam">n</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_maxiter</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t492" href="#t492">492</a></span><span class="t">            <span class="com"># form the function g with g(u) = 0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t493" href="#t493">493</a></span><span class="t">            <span class="nam">g</span> <span class="op">=</span> <span class="nam">u</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span> <span class="op">-</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">u</span> <span class="op">**</span> <span class="op">(</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">)</span> <span class="op">-</span> <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t494" href="#t494">494</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t495" href="#t495">495</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t496" href="#t496">496</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t497" href="#t497">497</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t498" href="#t498">498</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t499" href="#t499">499</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t500" href="#t500">500</a></span><span class="t"><span class="str">            Current time of the numerical solution is computed.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t495" href="#t495">495</a></span><span class="t">            <span class="com"># if g is close to 0, then we are done</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t496" href="#t496">496</a></span><span class="t">            <span class="com"># res = np.linalg.norm(g, np.inf)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t497" href="#t497">497</a></span><span class="t">            <span class="nam">res</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">linalg</span><span class="op">.</span><span class="nam">norm</span><span class="op">(</span><span class="nam">g</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">inf</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t498" href="#t498">498</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t499" href="#t499">499</a></span><span class="t">            <span class="key">if</span> <span class="nam">res</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_tol</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t500" href="#t500">500</a></span><span class="t">                <span class="key">break</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t501" href="#t501">501</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t502" href="#t502">502</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t503" href="#t503">503</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t504" href="#t504">504</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t505" href="#t505">505</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t506" href="#t506">506</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t507" href="#t507">507</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t508" href="#t508">508</a></span><span class="t">        <span class="nam">v</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t509" href="#t509">509</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">comp1</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">v</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t510" href="#t510">510</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">comp2</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="nam">v</span><span class="op">**</span><span class="nam">self</span><span class="op">.</span><span class="nam">nu</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t502" href="#t502">502</a></span><span class="t">            <span class="com"># assemble dg</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t503" href="#t503">503</a></span><span class="t">            <span class="nam">dg</span> <span class="op">=</span> <span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span> <span class="op">-</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">diags</span><span class="op">(</span><span class="op">(</span><span class="op">(</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span> <span class="op">*</span> <span class="nam">u</span><span class="op">**</span><span class="nam">nu</span><span class="op">)</span><span class="op">,</span> <span class="nam">offsets</span><span class="op">=</span><span class="num">0</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t504" href="#t504">504</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t505" href="#t505">505</a></span><span class="t">            <span class="com"># newton update: u1 = u0 - g/dg</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t506" href="#t506">506</a></span><span class="t">            <span class="com"># u -= spsolve(dg, g)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t507" href="#t507">507</a></span><span class="t">            <span class="nam">u</span> <span class="op">-=</span> <span class="nam">cg</span><span class="op">(</span><span class="nam">dg</span><span class="op">,</span> <span class="nam">g</span><span class="op">,</span> <span class="nam">x0</span><span class="op">=</span><span class="nam">z</span><span class="op">,</span> <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_tol</span><span class="op">,</span> <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">)</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t508" href="#t508">508</a></span><span class="t">            <span class="com"># increase iteration count</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t509" href="#t509">509</a></span><span class="t">            <span class="nam">n</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t510" href="#t510">510</a></span><span class="t">            <span class="com"># print(n, res)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t511" href="#t511">511</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t512" href="#t512">512</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t513" href="#t513">513</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t514" href="#t514">514</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system_1</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t515" href="#t515">515</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t516" href="#t516">516</a></span><span class="t"><span class="str">        Simple linear solver for :math:`(I-factor\cdot A)\vec{u}=\vec{rhs}`.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t512" href="#t512">512</a></span><span class="t">        <span class="com"># if n == self.newton_maxiter:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t513" href="#t513">513</a></span><span class="t">        <span class="com">#     raise ProblemError('Newton did not converge after %i iterations, error is %s' % (n, res))</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t514" href="#t514">514</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t515" href="#t515">515</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t516" href="#t516">516</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t517" href="#t517">517</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t518" href="#t518">518</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t519" href="#t519">519</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t520" href="#t520">520</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t521" href="#t521">521</a></span><span class="t"><span class="str">            Right-hand side for the linear system.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t522" href="#t522">522</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t523" href="#t523">523</a></span><span class="t"><span class="str">            Abbrev. for the local stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t524" href="#t524">524</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t525" href="#t525">525</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t526" href="#t526">526</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t527" href="#t527">527</a></span><span class="t"><span class="str">            Current time (e.g. for time-dependent BCs).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t518" href="#t518">518</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_ncalls</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t519" href="#t519">519</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_itercount</span> <span class="op">+=</span> <span class="nam">n</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t520" href="#t520">520</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t521" href="#t521">521</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t522" href="#t522">522</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t523" href="#t523">523</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t524" href="#t524">524</a></span><span class="t"><span class="com"># noinspection PyUnusedLocal</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t525" href="#t525">525</a></span><span class="t"><span class="key">class</span> <span class="nam">allencahn_multiimplicit</span><span class="op">(</span><span class="nam">allencahn_fullyimplicit</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t526" href="#t526">526</a></span><span class="t">    <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t527" href="#t527">527</a></span><span class="t"><span class="str">    Example implementing the two-dimensional Allen-Cahn equation with periodic boundary conditions :math:`u \in [-1, 1]^2`</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t528" href="#t528">528</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t529" href="#t529">529</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t530" href="#t530">530</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t531" href="#t531">531</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t532" href="#t532">532</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t533" href="#t533">533</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t534" href="#t534">534</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t535" href="#t535">535</a></span><span class="t">        <span class="key">class</span> <span class="nam">context</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t536" href="#t536">536</a></span><span class="t">            <span class="nam">num_iter</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t537" href="#t537">537</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t538" href="#t538">538</a></span><span class="t">        <span class="key">def</span> <span class="nam">callback</span><span class="op">(</span><span class="nam">xk</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t539" href="#t539">539</a></span><span class="t">            <span class="nam">context</span><span class="op">.</span><span class="nam">num_iter</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t540" href="#t540">540</a></span><span class="t">            <span class="key">return</span> <span class="nam">context</span><span class="op">.</span><span class="nam">num_iter</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t529" href="#t529">529</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t530" href="#t530">530</a></span><span class="t"><span class="str">        \frac{\partial u}{\partial t} = \Delta u + \frac{1}{\varepsilon^2} u (1 - u^\nu)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t531" href="#t531">531</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t532" href="#t532">532</a></span><span class="t"><span class="str">    for constant parameter :math:`\nu`. Initial condition are circles of the form</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t533" href="#t533">533</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t534" href="#t534">534</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t535" href="#t535">535</a></span><span class="t"><span class="str">        u({\bf x}, 0) = \tanh\left(\frac{r - \sqrt{x_i^2 + y_j^2}}{\sqrt{2}\varepsilon}\right)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t536" href="#t536">536</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t537" href="#t537">537</a></span><span class="t"><span class="str">    for :math:`i, j=0,..,N-1`, where :math:`N` is the number of spatial grid points. For time-stepping, the problem is</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t538" href="#t538">538</a></span><span class="t"><span class="str">    treated in *multi-implicit* fashion, i.e., the linear system containing the Laplacian is solved by the conjugate gradients</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t539" href="#t539">539</a></span><span class="t"><span class="str">    method, and the system containing the rest of the right-hand side will be solved by Newton's method.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t540" href="#t540">540</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t541" href="#t541">541</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t542" href="#t542">542</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t542" href="#t542">542</a></span><span class="t">    <span class="nam">dtype_f</span> <span class="op">=</span> <span class="nam">comp2_mesh</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t543" href="#t543">543</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t544" href="#t544">544</a></span><span class="t">        <span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t545" href="#t545">545</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t546" href="#t546">546</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">cg</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t547" href="#t547">547</a></span><span class="t">            <span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t548" href="#t548">548</a></span><span class="t">            <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t549" href="#t549">549</a></span><span class="t">            <span class="nam">x0</span><span class="op">=</span><span class="nam">u0</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t550" href="#t550">550</a></span><span class="t">            <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_tol</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t551" href="#t551">551</a></span><span class="t">            <span class="nam">maxiter</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_maxiter</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t552" href="#t552">552</a></span><span class="t">            <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t553" href="#t553">553</a></span><span class="t">            <span class="nam">callback</span><span class="op">=</span><span class="nam">callback</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t554" href="#t554">554</a></span><span class="t">        <span class="op">)</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t555" href="#t555">555</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t556" href="#t556">556</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">lin_ncalls</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t557" href="#t557">557</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">lin_itercount</span> <span class="op">+=</span> <span class="nam">context</span><span class="op">.</span><span class="nam">num_iter</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t558" href="#t558">558</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t559" href="#t559">559</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t560" href="#t560">560</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t561" href="#t561">561</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system_2</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t562" href="#t562">562</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t563" href="#t563">563</a></span><span class="t"><span class="str">        Simple Newton solver.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t544" href="#t544">544</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t545" href="#t545">545</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t546" href="#t546">546</a></span><span class="t"><span class="str">        Routine to evaluate the right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t547" href="#t547">547</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t548" href="#t548">548</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t549" href="#t549">549</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t550" href="#t550">550</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t551" href="#t551">551</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t552" href="#t552">552</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t553" href="#t553">553</a></span><span class="t"><span class="str">            Current time of the numerical solution is computed.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t554" href="#t554">554</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t555" href="#t555">555</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t556" href="#t556">556</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t557" href="#t557">557</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t558" href="#t558">558</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t559" href="#t559">559</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t560" href="#t560">560</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t561" href="#t561">561</a></span><span class="t">        <span class="nam">v</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t562" href="#t562">562</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">comp1</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">v</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t563" href="#t563">563</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">comp2</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="nam">v</span><span class="op">**</span><span class="nam">self</span><span class="op">.</span><span class="nam">nu</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t564" href="#t564">564</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t565" href="#t565">565</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t566" href="#t566">566</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t567" href="#t567">567</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t568" href="#t568">568</a></span><span class="t"><span class="str">            Right-hand side for the nonlinear system.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t569" href="#t569">569</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t570" href="#t570">570</a></span><span class="t"><span class="str">            Abbrev. for the node-to-node stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t571" href="#t571">571</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t572" href="#t572">572</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t573" href="#t573">573</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t574" href="#t574">574</a></span><span class="t"><span class="str">            Current time (required here for the BC).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t575" href="#t575">575</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t576" href="#t576">576</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t577" href="#t577">577</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t578" href="#t578">578</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t579" href="#t579">579</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t580" href="#t580">580</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t565" href="#t565">565</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t566" href="#t566">566</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t567" href="#t567">567</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system_1</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t568" href="#t568">568</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t569" href="#t569">569</a></span><span class="t"><span class="str">        Simple linear solver for :math:`(I-factor\cdot A)\vec{u}=\vec{rhs}`.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t570" href="#t570">570</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t571" href="#t571">571</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t572" href="#t572">572</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t573" href="#t573">573</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t574" href="#t574">574</a></span><span class="t"><span class="str">            Right-hand side for the linear system.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t575" href="#t575">575</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t576" href="#t576">576</a></span><span class="t"><span class="str">            Abbrev. for the local stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t577" href="#t577">577</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t578" href="#t578">578</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t579" href="#t579">579</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t580" href="#t580">580</a></span><span class="t"><span class="str">            Current time (e.g. for time-dependent BCs).</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t581" href="#t581">581</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t582" href="#t582">582</a></span><span class="t">        <span class="nam">u</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">u0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t583" href="#t583">583</a></span><span class="t">        <span class="nam">z</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t584" href="#t584">584</a></span><span class="t">        <span class="nam">nu</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nu</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t585" href="#t585">585</a></span><span class="t">        <span class="nam">eps2</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t586" href="#t586">586</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t587" href="#t587">587</a></span><span class="t">        <span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t588" href="#t588">588</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t589" href="#t589">589</a></span><span class="t">        <span class="com"># start newton iteration</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t590" href="#t590">590</a></span><span class="t">        <span class="nam">n</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t591" href="#t591">591</a></span><span class="t">        <span class="nam">res</span> <span class="op">=</span> <span class="num">99</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t592" href="#t592">592</a></span><span class="t">        <span class="key">while</span> <span class="nam">n</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_maxiter</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t593" href="#t593">593</a></span><span class="t">            <span class="com"># form the function g with g(u) = 0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t594" href="#t594">594</a></span><span class="t">            <span class="nam">g</span> <span class="op">=</span> <span class="nam">u</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">u</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="nam">u</span><span class="op">**</span><span class="nam">nu</span><span class="op">)</span><span class="op">)</span> <span class="op">-</span> <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t595" href="#t595">595</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t596" href="#t596">596</a></span><span class="t">            <span class="com"># if g is close to 0, then we are done</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t597" href="#t597">597</a></span><span class="t">            <span class="nam">res</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">linalg</span><span class="op">.</span><span class="nam">norm</span><span class="op">(</span><span class="nam">g</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">inf</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t582" href="#t582">582</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t583" href="#t583">583</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t584" href="#t584">584</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t585" href="#t585">585</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t586" href="#t586">586</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t587" href="#t587">587</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t588" href="#t588">588</a></span><span class="t">        <span class="key">class</span> <span class="nam">context</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t589" href="#t589">589</a></span><span class="t">            <span class="nam">num_iter</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t590" href="#t590">590</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t591" href="#t591">591</a></span><span class="t">        <span class="key">def</span> <span class="nam">callback</span><span class="op">(</span><span class="nam">xk</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t592" href="#t592">592</a></span><span class="t">            <span class="nam">context</span><span class="op">.</span><span class="nam">num_iter</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t593" href="#t593">593</a></span><span class="t">            <span class="key">return</span> <span class="nam">context</span><span class="op">.</span><span class="nam">num_iter</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t594" href="#t594">594</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t595" href="#t595">595</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t596" href="#t596">596</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t597" href="#t597">597</a></span><span class="t">        <span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t598" href="#t598">598</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t599" href="#t599">599</a></span><span class="t">            <span class="key">if</span> <span class="nam">res</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_tol</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t600" href="#t600">600</a></span><span class="t">                <span class="key">break</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t601" href="#t601">601</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t602" href="#t602">602</a></span><span class="t">            <span class="com"># assemble dg</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t603" href="#t603">603</a></span><span class="t">            <span class="nam">dg</span> <span class="op">=</span> <span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">diags</span><span class="op">(</span><span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="op">(</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span> <span class="op">*</span> <span class="nam">u</span><span class="op">**</span><span class="nam">nu</span><span class="op">)</span><span class="op">,</span> <span class="nam">offsets</span><span class="op">=</span><span class="num">0</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t604" href="#t604">604</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t605" href="#t605">605</a></span><span class="t">            <span class="com"># newton update: u1 = u0 - g/dg</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t606" href="#t606">606</a></span><span class="t">            <span class="com"># u -= spsolve(dg, g)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t607" href="#t607">607</a></span><span class="t">            <span class="nam">u</span> <span class="op">-=</span> <span class="nam">cg</span><span class="op">(</span><span class="nam">dg</span><span class="op">,</span> <span class="nam">g</span><span class="op">,</span> <span class="nam">x0</span><span class="op">=</span><span class="nam">z</span><span class="op">,</span> <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_tol</span><span class="op">,</span> <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">)</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t608" href="#t608">608</a></span><span class="t">            <span class="com"># increase iteration count</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t609" href="#t609">609</a></span><span class="t">            <span class="nam">n</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t610" href="#t610">610</a></span><span class="t">            <span class="com"># print(n, res)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t599" href="#t599">599</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">cg</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t600" href="#t600">600</a></span><span class="t">            <span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t601" href="#t601">601</a></span><span class="t">            <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t602" href="#t602">602</a></span><span class="t">            <span class="nam">x0</span><span class="op">=</span><span class="nam">u0</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t603" href="#t603">603</a></span><span class="t">            <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_tol</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t604" href="#t604">604</a></span><span class="t">            <span class="nam">maxiter</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_maxiter</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t605" href="#t605">605</a></span><span class="t">            <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t606" href="#t606">606</a></span><span class="t">            <span class="nam">callback</span><span class="op">=</span><span class="nam">callback</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t607" href="#t607">607</a></span><span class="t">        <span class="op">)</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t608" href="#t608">608</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t609" href="#t609">609</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">lin_ncalls</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t610" href="#t610">610</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">lin_itercount</span> <span class="op">+=</span> <span class="nam">context</span><span class="op">.</span><span class="nam">num_iter</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t611" href="#t611">611</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t612" href="#t612">612</a></span><span class="t">        <span class="com"># if n == self.newton_maxiter:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t613" href="#t613">613</a></span><span class="t">        <span class="com">#     raise ProblemError('Newton did not converge after %i iterations, error is %s' % (n, res))</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t614" href="#t614">614</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t615" href="#t615">615</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t616" href="#t616">616</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t612" href="#t612">612</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t613" href="#t613">613</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t614" href="#t614">614</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system_2</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t615" href="#t615">615</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t616" href="#t616">616</a></span><span class="t"><span class="str">        Simple Newton solver.</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t617" href="#t617">617</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t618" href="#t618">618</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_ncalls</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t619" href="#t619">619</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_itercount</span> <span class="op">+=</span> <span class="nam">n</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t620" href="#t620">620</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t621" href="#t621">621</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t622" href="#t622">622</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t623" href="#t623">623</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t624" href="#t624">624</a></span><span class="t"><span class="com"># noinspection PyUnusedLocal</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t625" href="#t625">625</a></span><span class="t"><span class="key">class</span> <span class="nam">allencahn_multiimplicit_v2</span><span class="op">(</span><span class="nam">allencahn_fullyimplicit</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t626" href="#t626">626</a></span><span class="t">    <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t627" href="#t627">627</a></span><span class="t"><span class="str">    This class implements the two-dimensional Allen-Cahn (AC) equation with periodic boundary conditions :math:`u \in [-1, 1]^2`</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t618" href="#t618">618</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t619" href="#t619">619</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t620" href="#t620">620</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t621" href="#t621">621</a></span><span class="t"><span class="str">            Right-hand side for the nonlinear system.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t622" href="#t622">622</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t623" href="#t623">623</a></span><span class="t"><span class="str">            Abbrev. for the node-to-node stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t624" href="#t624">624</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t625" href="#t625">625</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t626" href="#t626">626</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t627" href="#t627">627</a></span><span class="t"><span class="str">            Current time (required here for the BC).</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t628" href="#t628">628</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t629" href="#t629">629</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t630" href="#t630">630</a></span><span class="t"><span class="str">        \frac{\partial u}{\partial t} = \Delta u + \frac{1}{\varepsilon^2} u (1 - u^\nu)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t631" href="#t631">631</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t632" href="#t632">632</a></span><span class="t"><span class="str">    for constant parameter :math:`\nu`. The initial condition has the form of circles</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t633" href="#t633">633</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t634" href="#t634">634</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t635" href="#t635">635</a></span><span class="t"><span class="str">        u({\bf x}, 0) = \tanh\left(\frac{r - \sqrt{x_i^2 + y_j^2}}{\sqrt{2}\varepsilon}\right)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t636" href="#t636">636</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t637" href="#t637">637</a></span><span class="t"><span class="str">    for :math:`i, j=0,..,N-1`, where :math:`N` is the number of spatial grid points. For time-stepping, a special AC-splitting</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t638" href="#t638">638</a></span><span class="t"><span class="str">    is used here to get another kind of *semi-implicit* treatment of the problem: The term :math:`\Delta u - \frac{1}{\varepsilon^2} u^{\nu + 1}`</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t639" href="#t639">639</a></span><span class="t"><span class="str">    is handled implicitly and the nonlinear system including this part will be solved by Newton. :math:`\frac{1}{\varepsilon^2} u`</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t640" href="#t640">640</a></span><span class="t"><span class="str">    is solved by a linear solver provided by a ``SciPy`` routine.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t641" href="#t641">641</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t642" href="#t642">642</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t643" href="#t643">643</a></span><span class="t">    <span class="nam">dtype_f</span> <span class="op">=</span> <span class="nam">comp2_mesh</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t644" href="#t644">644</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t645" href="#t645">645</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t646" href="#t646">646</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t647" href="#t647">647</a></span><span class="t"><span class="str">        Routine to evaluate the right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t629" href="#t629">629</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t630" href="#t630">630</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t631" href="#t631">631</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t632" href="#t632">632</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t633" href="#t633">633</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t634" href="#t634">634</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t635" href="#t635">635</a></span><span class="t">        <span class="nam">u</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">u0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t636" href="#t636">636</a></span><span class="t">        <span class="nam">z</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t637" href="#t637">637</a></span><span class="t">        <span class="nam">nu</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nu</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t638" href="#t638">638</a></span><span class="t">        <span class="nam">eps2</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t639" href="#t639">639</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t640" href="#t640">640</a></span><span class="t">        <span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t641" href="#t641">641</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t642" href="#t642">642</a></span><span class="t">        <span class="com"># start newton iteration</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t643" href="#t643">643</a></span><span class="t">        <span class="nam">n</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t644" href="#t644">644</a></span><span class="t">        <span class="nam">res</span> <span class="op">=</span> <span class="num">99</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t645" href="#t645">645</a></span><span class="t">        <span class="key">while</span> <span class="nam">n</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_maxiter</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t646" href="#t646">646</a></span><span class="t">            <span class="com"># form the function g with g(u) = 0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t647" href="#t647">647</a></span><span class="t">            <span class="nam">g</span> <span class="op">=</span> <span class="nam">u</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">u</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="nam">u</span><span class="op">**</span><span class="nam">nu</span><span class="op">)</span><span class="op">)</span> <span class="op">-</span> <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t648" href="#t648">648</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t649" href="#t649">649</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t650" href="#t650">650</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t651" href="#t651">651</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t652" href="#t652">652</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t653" href="#t653">653</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t654" href="#t654">654</a></span><span class="t"><span class="str">            Current time of the numerical solution is computed.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t655" href="#t655">655</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t656" href="#t656">656</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t657" href="#t657">657</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t658" href="#t658">658</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t659" href="#t659">659</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t660" href="#t660">660</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t661" href="#t661">661</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t662" href="#t662">662</a></span><span class="t">        <span class="nam">v</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t663" href="#t663">663</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">comp1</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">v</span><span class="op">)</span> <span class="op">-</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span> <span class="op">**</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t664" href="#t664">664</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">comp2</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t665" href="#t665">665</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t666" href="#t666">666</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t649" href="#t649">649</a></span><span class="t">            <span class="com"># if g is close to 0, then we are done</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t650" href="#t650">650</a></span><span class="t">            <span class="nam">res</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">linalg</span><span class="op">.</span><span class="nam">norm</span><span class="op">(</span><span class="nam">g</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">inf</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t651" href="#t651">651</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t652" href="#t652">652</a></span><span class="t">            <span class="key">if</span> <span class="nam">res</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_tol</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t653" href="#t653">653</a></span><span class="t">                <span class="key">break</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t654" href="#t654">654</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t655" href="#t655">655</a></span><span class="t">            <span class="com"># assemble dg</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t656" href="#t656">656</a></span><span class="t">            <span class="nam">dg</span> <span class="op">=</span> <span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">diags</span><span class="op">(</span><span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="op">(</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span> <span class="op">*</span> <span class="nam">u</span><span class="op">**</span><span class="nam">nu</span><span class="op">)</span><span class="op">,</span> <span class="nam">offsets</span><span class="op">=</span><span class="num">0</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t657" href="#t657">657</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t658" href="#t658">658</a></span><span class="t">            <span class="com"># newton update: u1 = u0 - g/dg</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t659" href="#t659">659</a></span><span class="t">            <span class="com"># u -= spsolve(dg, g)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t660" href="#t660">660</a></span><span class="t">            <span class="nam">u</span> <span class="op">-=</span> <span class="nam">cg</span><span class="op">(</span><span class="nam">dg</span><span class="op">,</span> <span class="nam">g</span><span class="op">,</span> <span class="nam">x0</span><span class="op">=</span><span class="nam">z</span><span class="op">,</span> <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_tol</span><span class="op">,</span> <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">)</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t661" href="#t661">661</a></span><span class="t">            <span class="com"># increase iteration count</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t662" href="#t662">662</a></span><span class="t">            <span class="nam">n</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t663" href="#t663">663</a></span><span class="t">            <span class="com"># print(n, res)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t664" href="#t664">664</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t665" href="#t665">665</a></span><span class="t">        <span class="com"># if n == self.newton_maxiter:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t666" href="#t666">666</a></span><span class="t">        <span class="com">#     raise ProblemError('Newton did not converge after %i iterations, error is %s' % (n, res))</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t667" href="#t667">667</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t668" href="#t668">668</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system_1</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t669" href="#t669">669</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t670" href="#t670">670</a></span><span class="t"><span class="str">        Simple Newton solver.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t671" href="#t671">671</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t672" href="#t672">672</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t673" href="#t673">673</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t674" href="#t674">674</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t675" href="#t675">675</a></span><span class="t"><span class="str">            Right-hand side for the nonlinear system.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t676" href="#t676">676</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t677" href="#t677">677</a></span><span class="t"><span class="str">            Abbrev. for the node-to-node stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t678" href="#t678">678</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t679" href="#t679">679</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t680" href="#t680">680</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t681" href="#t681">681</a></span><span class="t"><span class="str">            Current time (required here for the BC).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t682" href="#t682">682</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t683" href="#t683">683</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t684" href="#t684">684</a></span><span class="t"><span class="str">        ------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t685" href="#t685">685</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t686" href="#t686">686</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t687" href="#t687">687</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t688" href="#t688">688</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t689" href="#t689">689</a></span><span class="t">        <span class="nam">u</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">u0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t690" href="#t690">690</a></span><span class="t">        <span class="nam">z</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t691" href="#t691">691</a></span><span class="t">        <span class="nam">nu</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nu</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t692" href="#t692">692</a></span><span class="t">        <span class="nam">eps2</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t693" href="#t693">693</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t694" href="#t694">694</a></span><span class="t">        <span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t668" href="#t668">668</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t669" href="#t669">669</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t670" href="#t670">670</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t671" href="#t671">671</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_ncalls</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t672" href="#t672">672</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_itercount</span> <span class="op">+=</span> <span class="nam">n</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t673" href="#t673">673</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t674" href="#t674">674</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t675" href="#t675">675</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t676" href="#t676">676</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t677" href="#t677">677</a></span><span class="t"><span class="com"># noinspection PyUnusedLocal</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t678" href="#t678">678</a></span><span class="t"><span class="key">class</span> <span class="nam">allencahn_multiimplicit_v2</span><span class="op">(</span><span class="nam">allencahn_fullyimplicit</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t679" href="#t679">679</a></span><span class="t">    <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t680" href="#t680">680</a></span><span class="t"><span class="str">    This class implements the two-dimensional Allen-Cahn (AC) equation with periodic boundary conditions :math:`u \in [-1, 1]^2`</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t681" href="#t681">681</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t682" href="#t682">682</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t683" href="#t683">683</a></span><span class="t"><span class="str">        \frac{\partial u}{\partial t} = \Delta u + \frac{1}{\varepsilon^2} u (1 - u^\nu)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t684" href="#t684">684</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t685" href="#t685">685</a></span><span class="t"><span class="str">    for constant parameter :math:`\nu`. The initial condition has the form of circles</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t686" href="#t686">686</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t687" href="#t687">687</a></span><span class="t"><span class="str">    .. math::</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t688" href="#t688">688</a></span><span class="t"><span class="str">        u({\bf x}, 0) = \tanh\left(\frac{r - \sqrt{x_i^2 + y_j^2}}{\sqrt{2}\varepsilon}\right)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t689" href="#t689">689</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t690" href="#t690">690</a></span><span class="t"><span class="str">    for :math:`i, j=0,..,N-1`, where :math:`N` is the number of spatial grid points. For time-stepping, a special AC-splitting</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t691" href="#t691">691</a></span><span class="t"><span class="str">    is used here to get another kind of *semi-implicit* treatment of the problem: The term :math:`\Delta u - \frac{1}{\varepsilon^2} u^{\nu + 1}`</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t692" href="#t692">692</a></span><span class="t"><span class="str">    is handled implicitly and the nonlinear system including this part will be solved by Newton. :math:`\frac{1}{\varepsilon^2} u`</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t693" href="#t693">693</a></span><span class="t"><span class="str">    is solved by a linear solver provided by a ``SciPy`` routine.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t694" href="#t694">694</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t695" href="#t695">695</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t696" href="#t696">696</a></span><span class="t">        <span class="com"># start newton iteration</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t697" href="#t697">697</a></span><span class="t">        <span class="nam">n</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t698" href="#t698">698</a></span><span class="t">        <span class="nam">res</span> <span class="op">=</span> <span class="num">99</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t699" href="#t699">699</a></span><span class="t">        <span class="key">while</span> <span class="nam">n</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_maxiter</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t700" href="#t700">700</a></span><span class="t">            <span class="com"># form the function g with g(u) = 0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t701" href="#t701">701</a></span><span class="t">            <span class="nam">g</span> <span class="op">=</span> <span class="nam">u</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span> <span class="op">-</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">u</span> <span class="op">**</span> <span class="op">(</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">)</span> <span class="op">-</span> <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t702" href="#t702">702</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t703" href="#t703">703</a></span><span class="t">            <span class="com"># if g is close to 0, then we are done</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t704" href="#t704">704</a></span><span class="t">            <span class="nam">res</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">linalg</span><span class="op">.</span><span class="nam">norm</span><span class="op">(</span><span class="nam">g</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">inf</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t705" href="#t705">705</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t706" href="#t706">706</a></span><span class="t">            <span class="key">if</span> <span class="nam">res</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_tol</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t707" href="#t707">707</a></span><span class="t">                <span class="key">break</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t696" href="#t696">696</a></span><span class="t">    <span class="nam">dtype_f</span> <span class="op">=</span> <span class="nam">comp2_mesh</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t697" href="#t697">697</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t698" href="#t698">698</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t699" href="#t699">699</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t700" href="#t700">700</a></span><span class="t"><span class="str">        Routine to evaluate the right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t701" href="#t701">701</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t702" href="#t702">702</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t703" href="#t703">703</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t704" href="#t704">704</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t705" href="#t705">705</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t706" href="#t706">706</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t707" href="#t707">707</a></span><span class="t"><span class="str">            Current time of the numerical solution is computed.</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t708" href="#t708">708</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t709" href="#t709">709</a></span><span class="t">            <span class="com"># assemble dg</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t710" href="#t710">710</a></span><span class="t">            <span class="nam">dg</span> <span class="op">=</span> <span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span> <span class="op">-</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">diags</span><span class="op">(</span><span class="op">(</span><span class="op">(</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span> <span class="op">*</span> <span class="nam">u</span><span class="op">**</span><span class="nam">nu</span><span class="op">)</span><span class="op">,</span> <span class="nam">offsets</span><span class="op">=</span><span class="num">0</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t711" href="#t711">711</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t712" href="#t712">712</a></span><span class="t">            <span class="com"># newton update: u1 = u0 - g/dg</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t713" href="#t713">713</a></span><span class="t">            <span class="com"># u -= spsolve(dg, g)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t714" href="#t714">714</a></span><span class="t">            <span class="nam">u</span> <span class="op">-=</span> <span class="nam">cg</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t715" href="#t715">715</a></span><span class="t">                <span class="nam">dg</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t716" href="#t716">716</a></span><span class="t">                <span class="nam">g</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t717" href="#t717">717</a></span><span class="t">                <span class="nam">x0</span><span class="op">=</span><span class="nam">z</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t718" href="#t718">718</a></span><span class="t">                <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_tol</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t719" href="#t719">719</a></span><span class="t">                <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t720" href="#t720">720</a></span><span class="t">            <span class="op">)</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t721" href="#t721">721</a></span><span class="t">            <span class="com"># increase iteration count</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t722" href="#t722">722</a></span><span class="t">            <span class="nam">n</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t723" href="#t723">723</a></span><span class="t">            <span class="com"># print(n, res)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t709" href="#t709">709</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t710" href="#t710">710</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t711" href="#t711">711</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t712" href="#t712">712</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t713" href="#t713">713</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t714" href="#t714">714</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t715" href="#t715">715</a></span><span class="t">        <span class="nam">v</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t716" href="#t716">716</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">comp1</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">v</span><span class="op">)</span> <span class="op">-</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span> <span class="op">**</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t717" href="#t717">717</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">comp2</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span> <span class="op">*</span> <span class="nam">v</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t718" href="#t718">718</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t719" href="#t719">719</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t720" href="#t720">720</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t721" href="#t721">721</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system_1</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t722" href="#t722">722</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t723" href="#t723">723</a></span><span class="t"><span class="str">        Simple Newton solver.</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t724" href="#t724">724</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t725" href="#t725">725</a></span><span class="t">        <span class="com"># if n == self.newton_maxiter:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t726" href="#t726">726</a></span><span class="t">        <span class="com">#     raise ProblemError('Newton did not converge after %i iterations, error is %s' % (n, res))</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t727" href="#t727">727</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t728" href="#t728">728</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t729" href="#t729">729</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t730" href="#t730">730</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t731" href="#t731">731</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_ncalls</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t732" href="#t732">732</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_itercount</span> <span class="op">+=</span> <span class="nam">n</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t733" href="#t733">733</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t734" href="#t734">734</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t725" href="#t725">725</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t726" href="#t726">726</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t727" href="#t727">727</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t728" href="#t728">728</a></span><span class="t"><span class="str">            Right-hand side for the nonlinear system.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t729" href="#t729">729</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t730" href="#t730">730</a></span><span class="t"><span class="str">            Abbrev. for the node-to-node stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t731" href="#t731">731</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t732" href="#t732">732</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t733" href="#t733">733</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t734" href="#t734">734</a></span><span class="t"><span class="str">            Current time (required here for the BC).</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t735" href="#t735">735</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t736" href="#t736">736</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system_2</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t737" href="#t737">737</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t738" href="#t738">738</a></span><span class="t"><span class="str">        Simple linear solver for :math:`(I-factor\cdot A)\vec{u}=\vec{rhs}`.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t739" href="#t739">739</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t740" href="#t740">740</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t741" href="#t741">741</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t742" href="#t742">742</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t743" href="#t743">743</a></span><span class="t"><span class="str">            Right-hand side for the linear system.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t744" href="#t744">744</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t745" href="#t745">745</a></span><span class="t"><span class="str">            Abbrev. for the local stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t746" href="#t746">746</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t747" href="#t747">747</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t748" href="#t748">748</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t749" href="#t749">749</a></span><span class="t"><span class="str">            Current time (e.g. for time-dependent BCs).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t750" href="#t750">750</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t751" href="#t751">751</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t752" href="#t752">752</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t753" href="#t753">753</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t754" href="#t754">754</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t755" href="#t755">755</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t756" href="#t756">756</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t757" href="#t757">757</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t736" href="#t736">736</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t737" href="#t737">737</a></span><span class="t"><span class="str">        ------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t738" href="#t738">738</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t739" href="#t739">739</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t740" href="#t740">740</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t741" href="#t741">741</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t742" href="#t742">742</a></span><span class="t">        <span class="nam">u</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">u0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t743" href="#t743">743</a></span><span class="t">        <span class="nam">z</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t744" href="#t744">744</a></span><span class="t">        <span class="nam">nu</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nu</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t745" href="#t745">745</a></span><span class="t">        <span class="nam">eps2</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t746" href="#t746">746</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t747" href="#t747">747</a></span><span class="t">        <span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t748" href="#t748">748</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t749" href="#t749">749</a></span><span class="t">        <span class="com"># start newton iteration</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t750" href="#t750">750</a></span><span class="t">        <span class="nam">n</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t751" href="#t751">751</a></span><span class="t">        <span class="nam">res</span> <span class="op">=</span> <span class="num">99</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t752" href="#t752">752</a></span><span class="t">        <span class="key">while</span> <span class="nam">n</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_maxiter</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t753" href="#t753">753</a></span><span class="t">            <span class="com"># form the function g with g(u) = 0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t754" href="#t754">754</a></span><span class="t">            <span class="nam">g</span> <span class="op">=</span> <span class="nam">u</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span> <span class="op">-</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">u</span> <span class="op">**</span> <span class="op">(</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span><span class="op">)</span> <span class="op">-</span> <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t755" href="#t755">755</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t756" href="#t756">756</a></span><span class="t">            <span class="com"># if g is close to 0, then we are done</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t757" href="#t757">757</a></span><span class="t">            <span class="nam">res</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">linalg</span><span class="op">.</span><span class="nam">norm</span><span class="op">(</span><span class="nam">g</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">inf</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t758" href="#t758">758</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t759" href="#t759">759</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span><span class="op">)</span> <span class="op">*</span> <span class="nam">rhs</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t760" href="#t760">760</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t759" href="#t759">759</a></span><span class="t">            <span class="key">if</span> <span class="nam">res</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_tol</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t760" href="#t760">760</a></span><span class="t">                <span class="key">break</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t761" href="#t761">761</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t762" href="#t762">762</a></span><span class="t">            <span class="com"># assemble dg</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t763" href="#t763">763</a></span><span class="t">            <span class="nam">dg</span> <span class="op">=</span> <span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span> <span class="op">-</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">eps2</span> <span class="op">*</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">diags</span><span class="op">(</span><span class="op">(</span><span class="op">(</span><span class="nam">nu</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span> <span class="op">*</span> <span class="nam">u</span><span class="op">**</span><span class="nam">nu</span><span class="op">)</span><span class="op">,</span> <span class="nam">offsets</span><span class="op">=</span><span class="num">0</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t764" href="#t764">764</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t765" href="#t765">765</a></span><span class="t">            <span class="com"># newton update: u1 = u0 - g/dg</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t766" href="#t766">766</a></span><span class="t">            <span class="com"># u -= spsolve(dg, g)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t767" href="#t767">767</a></span><span class="t">            <span class="nam">u</span> <span class="op">-=</span> <span class="nam">cg</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t768" href="#t768">768</a></span><span class="t">                <span class="nam">dg</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t769" href="#t769">769</a></span><span class="t">                <span class="nam">g</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t770" href="#t770">770</a></span><span class="t">                <span class="nam">x0</span><span class="op">=</span><span class="nam">z</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t771" href="#t771">771</a></span><span class="t">                <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lin_tol</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t772" href="#t772">772</a></span><span class="t">                <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t773" href="#t773">773</a></span><span class="t">            <span class="op">)</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t774" href="#t774">774</a></span><span class="t">            <span class="com"># increase iteration count</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t775" href="#t775">775</a></span><span class="t">            <span class="nam">n</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t776" href="#t776">776</a></span><span class="t">            <span class="com"># print(n, res)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t777" href="#t777">777</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t778" href="#t778">778</a></span><span class="t">        <span class="com"># if n == self.newton_maxiter:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t779" href="#t779">779</a></span><span class="t">        <span class="com">#     raise ProblemError('Newton did not converge after %i iterations, error is %s' % (n, res))</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t780" href="#t780">780</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t781" href="#t781">781</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t782" href="#t782">782</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t783" href="#t783">783</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t784" href="#t784">784</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_ncalls</span> <span class="op">+=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t785" href="#t785">785</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">newton_itercount</span> <span class="op">+=</span> <span class="nam">n</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t786" href="#t786">786</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t787" href="#t787">787</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t788" href="#t788">788</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t789" href="#t789">789</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system_2</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t790" href="#t790">790</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t791" href="#t791">791</a></span><span class="t"><span class="str">        Simple linear solver for :math:`(I-factor\cdot A)\vec{u}=\vec{rhs}`.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t792" href="#t792">792</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t793" href="#t793">793</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t794" href="#t794">794</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t795" href="#t795">795</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t796" href="#t796">796</a></span><span class="t"><span class="str">            Right-hand side for the linear system.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t797" href="#t797">797</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t798" href="#t798">798</a></span><span class="t"><span class="str">            Abbrev. for the local stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t799" href="#t799">799</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t800" href="#t800">800</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t801" href="#t801">801</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t802" href="#t802">802</a></span><span class="t"><span class="str">            Current time (e.g. for time-dependent BCs).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t803" href="#t803">803</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t804" href="#t804">804</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t805" href="#t805">805</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t806" href="#t806">806</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t807" href="#t807">807</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t808" href="#t808">808</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t809" href="#t809">809</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t810" href="#t810">810</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t811" href="#t811">811</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t812" href="#t812">812</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">/</span> <span class="op">(</span><span class="num">1.0</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="num">1.0</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eps</span><span class="op">**</span><span class="num">2</span><span class="op">)</span> <span class="op">*</span> <span class="nam">rhs</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t813" href="#t813">813</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
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@@ -142,540 +142,546 @@ <h2>
     <p class="pln"><span class="n"><a id="t60" href="#t60">60</a></span><span class="t"><span class="str">        Maximum number of linear iterations inside the Newton solver.</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t61" href="#t61">61</a></span><span class="t"><span class="str">    direct_solver : bool, optional</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t62" href="#t62">62</a></span><span class="t"><span class="str">        Indicates if a direct solver should be used.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t63" href="#t63">63</a></span><span class="t"><span class="str">    reference_sol_type : str, optional</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t64" href="#t64">64</a></span><span class="t"><span class="str">        Indicates which method should be used to compute a reference solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t65" href="#t65">65</a></span><span class="t"><span class="str">        Choose between ``'scipy'``, ``'SDC'``, or ``'DIRK'``.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t66" href="#t66">66</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t67" href="#t67">67</a></span><span class="t"><span class="str">    Attributes</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t68" href="#t68">68</a></span><span class="t"><span class="str">    ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t69" href="#t69">69</a></span><span class="t"><span class="str">    A : sparse matrix (CSC)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t70" href="#t70">70</a></span><span class="t"><span class="str">        FD discretization matrix of the ND grad operator.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t71" href="#t71">71</a></span><span class="t"><span class="str">    Id : sparse matrix (CSC)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t72" href="#t72">72</a></span><span class="t"><span class="str">        Identity matrix of the same dimension as A.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t73" href="#t73">73</a></span><span class="t"><span class="str">    dx : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t74" href="#t74">74</a></span><span class="t"><span class="str">        Distance between two spatial nodes.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t75" href="#t75">75</a></span><span class="t"><span class="str">    xv : np.1darray</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t76" href="#t76">76</a></span><span class="t"><span class="str">        Spatial grid values.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t77" href="#t77">77</a></span><span class="t"><span class="str">    leak : np.1darray of bool</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t78" href="#t78">78</a></span><span class="t"><span class="str">        Indicates the leak.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t79" href="#t79">79</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t80" href="#t80">80</a></span><span class="t"><span class="str">    References</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t81" href="#t81">81</a></span><span class="t"><span class="str">    ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t82" href="#t82">82</a></span><span class="t"><span class="str">    .. [1] Thermal thin shell approximation towards finite element quench simulation. E. Schnaubelt, M. Wozniak, S. Sch&#246;ps.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t83" href="#t83">83</a></span><span class="t"><span class="str">       Supercond. Sci. Technol. 36 044004. DOI 10.1088/1361-6668/acbeea</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t84" href="#t84">84</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t85" href="#t85">85</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t86" href="#t86">86</a></span><span class="t">    <span class="nam">dtype_u</span> <span class="op">=</span> <span class="nam">mesh</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t87" href="#t87">87</a></span><span class="t">    <span class="nam">dtype_f</span> <span class="op">=</span> <span class="nam">mesh</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t88" href="#t88">88</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t89" href="#t89">89</a></span><span class="t">    <span class="key">def</span> <span class="nam">__init__</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t90" href="#t90">90</a></span><span class="t">        <span class="nam">self</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t91" href="#t91">91</a></span><span class="t">        <span class="nam">Cv</span><span class="op">=</span><span class="num">1000.0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t92" href="#t92">92</a></span><span class="t">        <span class="nam">K</span><span class="op">=</span><span class="num">1000.0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t93" href="#t93">93</a></span><span class="t">        <span class="nam">u_thresh</span><span class="op">=</span><span class="num">3e-2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t94" href="#t94">94</a></span><span class="t">        <span class="nam">u_max</span><span class="op">=</span><span class="num">6e-2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t95" href="#t95">95</a></span><span class="t">        <span class="nam">Q_max</span><span class="op">=</span><span class="num">1.0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t96" href="#t96">96</a></span><span class="t">        <span class="nam">leak_range</span><span class="op">=</span><span class="op">(</span><span class="num">0.45</span><span class="op">,</span> <span class="num">0.55</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t97" href="#t97">97</a></span><span class="t">        <span class="nam">leak_type</span><span class="op">=</span><span class="str">'linear'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t98" href="#t98">98</a></span><span class="t">        <span class="nam">leak_transition</span><span class="op">=</span><span class="str">'step'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t99" href="#t99">99</a></span><span class="t">        <span class="nam">order</span><span class="op">=</span><span class="num">2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t100" href="#t100">100</a></span><span class="t">        <span class="nam">stencil_type</span><span class="op">=</span><span class="str">'center'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t101" href="#t101">101</a></span><span class="t">        <span class="nam">bc</span><span class="op">=</span><span class="str">'neumann-zero'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t102" href="#t102">102</a></span><span class="t">        <span class="nam">nvars</span><span class="op">=</span><span class="num">2</span><span class="op">**</span><span class="num">7</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t103" href="#t103">103</a></span><span class="t">        <span class="nam">newton_tol</span><span class="op">=</span><span class="num">1e-8</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t104" href="#t104">104</a></span><span class="t">        <span class="nam">newton_maxiter</span><span class="op">=</span><span class="num">99</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t105" href="#t105">105</a></span><span class="t">        <span class="nam">lintol</span><span class="op">=</span><span class="num">1e-8</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t106" href="#t106">106</a></span><span class="t">        <span class="nam">liniter</span><span class="op">=</span><span class="num">99</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t107" href="#t107">107</a></span><span class="t">        <span class="nam">direct_solver</span><span class="op">=</span><span class="key">True</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t108" href="#t108">108</a></span><span class="t">        <span class="nam">inexact_linear_ratio</span><span class="op">=</span><span class="key">None</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t109" href="#t109">109</a></span><span class="t">        <span class="nam">reference_sol_type</span><span class="op">=</span><span class="str">'scipy'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t110" href="#t110">110</a></span><span class="t">    <span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t111" href="#t111">111</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t112" href="#t112">112</a></span><span class="t"><span class="str">        Initialization routine</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t113" href="#t113">113</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t114" href="#t114">114</a></span><span class="t"><span class="str">        Args:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t115" href="#t115">115</a></span><span class="t"><span class="str">            problem_params (dict): custom parameters for the example</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t116" href="#t116">116</a></span><span class="t"><span class="str">            dtype_u: mesh data type (will be passed parent class)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t117" href="#t117">117</a></span><span class="t"><span class="str">            dtype_f: mesh data type (will be passed parent class)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t118" href="#t118">118</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t119" href="#t119">119</a></span><span class="t">        <span class="com"># invoke super init, passing number of dofs, dtype_u and dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t120" href="#t120">120</a></span><span class="t">        <span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">__init__</span><span class="op">(</span><span class="nam">init</span><span class="op">=</span><span class="op">(</span><span class="nam">nvars</span><span class="op">,</span> <span class="key">None</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">dtype</span><span class="op">(</span><span class="str">'float64'</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t121" href="#t121">121</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">_makeAttributeAndRegister</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t122" href="#t122">122</a></span><span class="t">            <span class="str">'Cv'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t123" href="#t123">123</a></span><span class="t">            <span class="str">'K'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t124" href="#t124">124</a></span><span class="t">            <span class="str">'u_thresh'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t125" href="#t125">125</a></span><span class="t">            <span class="str">'u_max'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t126" href="#t126">126</a></span><span class="t">            <span class="str">'Q_max'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t127" href="#t127">127</a></span><span class="t">            <span class="str">'leak_range'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t128" href="#t128">128</a></span><span class="t">            <span class="str">'leak_type'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t129" href="#t129">129</a></span><span class="t">            <span class="str">'leak_transition'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t130" href="#t130">130</a></span><span class="t">            <span class="str">'order'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t131" href="#t131">131</a></span><span class="t">            <span class="str">'stencil_type'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t132" href="#t132">132</a></span><span class="t">            <span class="str">'bc'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t133" href="#t133">133</a></span><span class="t">            <span class="str">'nvars'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t134" href="#t134">134</a></span><span class="t">            <span class="str">'direct_solver'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t135" href="#t135">135</a></span><span class="t">            <span class="str">'reference_sol_type'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t136" href="#t136">136</a></span><span class="t">            <span class="nam">localVars</span><span class="op">=</span><span class="nam">locals</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t137" href="#t137">137</a></span><span class="t">            <span class="nam">readOnly</span><span class="op">=</span><span class="key">True</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t138" href="#t138">138</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t139" href="#t139">139</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">_makeAttributeAndRegister</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t140" href="#t140">140</a></span><span class="t">            <span class="str">'newton_tol'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t141" href="#t141">141</a></span><span class="t">            <span class="str">'newton_maxiter'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t142" href="#t142">142</a></span><span class="t">            <span class="str">'lintol'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t143" href="#t143">143</a></span><span class="t">            <span class="str">'liniter'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t144" href="#t144">144</a></span><span class="t">            <span class="str">'inexact_linear_ratio'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t145" href="#t145">145</a></span><span class="t">            <span class="nam">localVars</span><span class="op">=</span><span class="nam">locals</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t146" href="#t146">146</a></span><span class="t">            <span class="nam">readOnly</span><span class="op">=</span><span class="key">False</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t147" href="#t147">147</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t148" href="#t148">148</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t149" href="#t149">149</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">_makeAttributeAndRegister</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t150" href="#t150">150</a></span><span class="t">            <span class="str">'newton_tol'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t151" href="#t151">151</a></span><span class="t">            <span class="str">'newton_maxiter'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t152" href="#t152">152</a></span><span class="t">            <span class="str">'lintol'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t153" href="#t153">153</a></span><span class="t">            <span class="str">'liniter'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t154" href="#t154">154</a></span><span class="t">            <span class="str">'direct_solver'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t155" href="#t155">155</a></span><span class="t">            <span class="nam">localVars</span><span class="op">=</span><span class="nam">locals</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t156" href="#t156">156</a></span><span class="t">            <span class="nam">readOnly</span><span class="op">=</span><span class="key">False</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t157" href="#t157">157</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t158" href="#t158">158</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t159" href="#t159">159</a></span><span class="t">        <span class="com"># setup finite difference discretization from problem helper</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t160" href="#t160">160</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">dx</span><span class="op">,</span> <span class="nam">xvalues</span> <span class="op">=</span> <span class="nam">problem_helper</span><span class="op">.</span><span class="nam">get_1d_grid</span><span class="op">(</span><span class="nam">size</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">,</span> <span class="nam">bc</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">bc</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t161" href="#t161">161</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t162" href="#t162">162</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">b</span> <span class="op">=</span> <span class="nam">problem_helper</span><span class="op">.</span><span class="nam">get_finite_difference_matrix</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t163" href="#t163">163</a></span><span class="t">            <span class="nam">derivative</span><span class="op">=</span><span class="num">2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t164" href="#t164">164</a></span><span class="t">            <span class="nam">order</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">order</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t165" href="#t165">165</a></span><span class="t">            <span class="nam">stencil_type</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">stencil_type</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t166" href="#t166">166</a></span><span class="t">            <span class="nam">dx</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">dx</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t167" href="#t167">167</a></span><span class="t">            <span class="nam">size</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t168" href="#t168">168</a></span><span class="t">            <span class="nam">dim</span><span class="op">=</span><span class="num">1</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t169" href="#t169">169</a></span><span class="t">            <span class="nam">bc</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">bc</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t170" href="#t170">170</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t171" href="#t171">171</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">A</span> <span class="op">*=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">K</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">Cv</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t172" href="#t172">172</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t173" href="#t173">173</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">xv</span> <span class="op">=</span> <span class="nam">xvalues</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t174" href="#t174">174</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">np</span><span class="op">.</span><span class="nam">prod</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span><span class="op">,</span> <span class="nam">format</span><span class="op">=</span><span class="str">'csc'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t175" href="#t175">175</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t176" href="#t176">176</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">leak</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">logical_and</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">xv</span> <span class="op">></span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_range</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">xv</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_range</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t177" href="#t177">177</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t178" href="#t178">178</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'newton'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">WorkCounter</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t179" href="#t179">179</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'rhs'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">WorkCounter</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t180" href="#t180">180</a></span><span class="t">        <span class="key">if</span> <span class="key">not</span> <span class="nam">self</span><span class="op">.</span><span class="nam">direct_solver</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t181" href="#t181">181</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'linear'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">WorkCounter</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t182" href="#t182">182</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t183" href="#t183">183</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f_non_linear</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t184" href="#t184">184</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t185" href="#t185">185</a></span><span class="t"><span class="str">        Get the non-linear part of f.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t186" href="#t186">186</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t187" href="#t187">187</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t188" href="#t188">188</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t189" href="#t189">189</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t190" href="#t190">190</a></span><span class="t"><span class="str">            Current values of the numerical solution:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t191" href="#t191">191</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t192" href="#t192">192</a></span><span class="t"><span class="str">            Current time at which the numerical solution is computed.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t193" href="#t193">193</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t194" href="#t194">194</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t195" href="#t195">195</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t196" href="#t196">196</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t197" href="#t197">197</a></span><span class="t"><span class="str">            The non-linear part of the right-hand side.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t198" href="#t198">198</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t199" href="#t199">199</a></span><span class="t">        <span class="nam">u_thresh</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">u_thresh</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t200" href="#t200">200</a></span><span class="t">        <span class="nam">u_max</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">u_max</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t201" href="#t201">201</a></span><span class="t">        <span class="nam">Q_max</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">Q_max</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t202" href="#t202">202</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t203" href="#t203">203</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t204" href="#t204">204</a></span><span class="t">        <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_type</span> <span class="op">==</span> <span class="str">'linear'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t205" href="#t205">205</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="nam">u</span> <span class="op">-</span> <span class="nam">u_thresh</span><span class="op">)</span> <span class="op">/</span> <span class="op">(</span><span class="nam">u_max</span> <span class="op">-</span> <span class="nam">u_thresh</span><span class="op">)</span> <span class="op">*</span> <span class="nam">Q_max</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t206" href="#t206">206</a></span><span class="t">        <span class="key">elif</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_type</span> <span class="op">==</span> <span class="str">'exponential'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t207" href="#t207">207</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">Q_max</span> <span class="op">*</span> <span class="op">(</span><span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span> <span class="op">-</span> <span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u_thresh</span><span class="op">)</span><span class="op">)</span> <span class="op">/</span> <span class="op">(</span><span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u_max</span><span class="op">)</span> <span class="op">-</span> <span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u_thresh</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t208" href="#t208">208</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t209" href="#t209">209</a></span><span class="t">            <span class="key">raise</span> <span class="nam">NotImplementedError</span><span class="op">(</span><span class="str">f'Leak type \"{self.leak_type}\" not implemented!'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t210" href="#t210">210</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t211" href="#t211">211</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="nam">u</span> <span class="op">&lt;</span> <span class="nam">u_thresh</span><span class="op">]</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t212" href="#t212">212</a></span><span class="t">        <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_transition</span> <span class="op">==</span> <span class="str">'step'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t213" href="#t213">213</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">leak</span><span class="op">]</span> <span class="op">=</span> <span class="nam">Q_max</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t214" href="#t214">214</a></span><span class="t">        <span class="key">elif</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_transition</span> <span class="op">==</span> <span class="str">'Gaussian'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t215" href="#t215">215</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">max</span><span class="op">(</span><span class="op">[</span><span class="nam">me</span><span class="op">,</span> <span class="nam">Q_max</span> <span class="op">*</span> <span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="op">-</span><span class="op">(</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">xv</span> <span class="op">-</span> <span class="num">0.5</span><span class="op">)</span> <span class="op">**</span> <span class="num">2</span><span class="op">)</span> <span class="op">/</span> <span class="num">3e-2</span><span class="op">)</span><span class="op">]</span><span class="op">,</span> <span class="nam">axis</span><span class="op">=</span><span class="num">0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t216" href="#t216">216</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t217" href="#t217">217</a></span><span class="t">            <span class="key">raise</span> <span class="nam">NotImplementedError</span><span class="op">(</span><span class="str">f'Leak transition \"{self.leak_transition}\" not implemented!'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t218" href="#t218">218</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t219" href="#t219">219</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="nam">u</span> <span class="op">>=</span> <span class="nam">u_max</span><span class="op">]</span> <span class="op">=</span> <span class="nam">Q_max</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t220" href="#t220">220</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t221" href="#t221">221</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">/=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">Cv</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t222" href="#t222">222</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t223" href="#t223">223</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t63" href="#t63">63</a></span><span class="t"><span class="str">    inexact_linear_ratio : float, optional</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t64" href="#t64">64</a></span><span class="t"><span class="str">        Ratio of tolerance of linear solver to the Newton residual, overrides `lintol`</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t65" href="#t65">65</a></span><span class="t"><span class="str">    min_lintol : float, optional</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t66" href="#t66">66</a></span><span class="t"><span class="str">        Minimal tolerance for the linear solver</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t67" href="#t67">67</a></span><span class="t"><span class="str">    reference_sol_type : str, optional</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t68" href="#t68">68</a></span><span class="t"><span class="str">        Indicates which method should be used to compute a reference solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t69" href="#t69">69</a></span><span class="t"><span class="str">        Choose between ``'scipy'``, ``'SDC'``, or ``'DIRK'``.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t70" href="#t70">70</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t71" href="#t71">71</a></span><span class="t"><span class="str">    Attributes</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t72" href="#t72">72</a></span><span class="t"><span class="str">    ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t73" href="#t73">73</a></span><span class="t"><span class="str">    A : sparse matrix (CSC)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t74" href="#t74">74</a></span><span class="t"><span class="str">        FD discretization matrix of the ND grad operator.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t75" href="#t75">75</a></span><span class="t"><span class="str">    Id : sparse matrix (CSC)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t76" href="#t76">76</a></span><span class="t"><span class="str">        Identity matrix of the same dimension as A.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t77" href="#t77">77</a></span><span class="t"><span class="str">    dx : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t78" href="#t78">78</a></span><span class="t"><span class="str">        Distance between two spatial nodes.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t79" href="#t79">79</a></span><span class="t"><span class="str">    xv : np.1darray</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t80" href="#t80">80</a></span><span class="t"><span class="str">        Spatial grid values.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t81" href="#t81">81</a></span><span class="t"><span class="str">    leak : np.1darray of bool</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t82" href="#t82">82</a></span><span class="t"><span class="str">        Indicates the leak.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t83" href="#t83">83</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t84" href="#t84">84</a></span><span class="t"><span class="str">    References</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t85" href="#t85">85</a></span><span class="t"><span class="str">    ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t86" href="#t86">86</a></span><span class="t"><span class="str">    .. [1] Thermal thin shell approximation towards finite element quench simulation. E. Schnaubelt, M. Wozniak, S. Sch&#246;ps.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t87" href="#t87">87</a></span><span class="t"><span class="str">       Supercond. Sci. Technol. 36 044004. DOI 10.1088/1361-6668/acbeea</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t88" href="#t88">88</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t89" href="#t89">89</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t90" href="#t90">90</a></span><span class="t">    <span class="nam">dtype_u</span> <span class="op">=</span> <span class="nam">mesh</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t91" href="#t91">91</a></span><span class="t">    <span class="nam">dtype_f</span> <span class="op">=</span> <span class="nam">mesh</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t92" href="#t92">92</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t93" href="#t93">93</a></span><span class="t">    <span class="key">def</span> <span class="nam">__init__</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t94" href="#t94">94</a></span><span class="t">        <span class="nam">self</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t95" href="#t95">95</a></span><span class="t">        <span class="nam">Cv</span><span class="op">=</span><span class="num">1000.0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t96" href="#t96">96</a></span><span class="t">        <span class="nam">K</span><span class="op">=</span><span class="num">1000.0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t97" href="#t97">97</a></span><span class="t">        <span class="nam">u_thresh</span><span class="op">=</span><span class="num">3e-2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t98" href="#t98">98</a></span><span class="t">        <span class="nam">u_max</span><span class="op">=</span><span class="num">6e-2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t99" href="#t99">99</a></span><span class="t">        <span class="nam">Q_max</span><span class="op">=</span><span class="num">1.0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t100" href="#t100">100</a></span><span class="t">        <span class="nam">leak_range</span><span class="op">=</span><span class="op">(</span><span class="num">0.45</span><span class="op">,</span> <span class="num">0.55</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t101" href="#t101">101</a></span><span class="t">        <span class="nam">leak_type</span><span class="op">=</span><span class="str">'linear'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t102" href="#t102">102</a></span><span class="t">        <span class="nam">leak_transition</span><span class="op">=</span><span class="str">'step'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t103" href="#t103">103</a></span><span class="t">        <span class="nam">order</span><span class="op">=</span><span class="num">2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t104" href="#t104">104</a></span><span class="t">        <span class="nam">stencil_type</span><span class="op">=</span><span class="str">'center'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t105" href="#t105">105</a></span><span class="t">        <span class="nam">bc</span><span class="op">=</span><span class="str">'neumann-zero'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t106" href="#t106">106</a></span><span class="t">        <span class="nam">nvars</span><span class="op">=</span><span class="num">2</span><span class="op">**</span><span class="num">7</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t107" href="#t107">107</a></span><span class="t">        <span class="nam">newton_tol</span><span class="op">=</span><span class="num">1e-8</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t108" href="#t108">108</a></span><span class="t">        <span class="nam">newton_maxiter</span><span class="op">=</span><span class="num">99</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t109" href="#t109">109</a></span><span class="t">        <span class="nam">lintol</span><span class="op">=</span><span class="num">1e-8</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t110" href="#t110">110</a></span><span class="t">        <span class="nam">liniter</span><span class="op">=</span><span class="num">99</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t111" href="#t111">111</a></span><span class="t">        <span class="nam">direct_solver</span><span class="op">=</span><span class="key">True</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t112" href="#t112">112</a></span><span class="t">        <span class="nam">inexact_linear_ratio</span><span class="op">=</span><span class="key">None</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t113" href="#t113">113</a></span><span class="t">        <span class="nam">min_lintol</span><span class="op">=</span><span class="num">1e-12</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t114" href="#t114">114</a></span><span class="t">        <span class="nam">reference_sol_type</span><span class="op">=</span><span class="str">'scipy'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t115" href="#t115">115</a></span><span class="t">    <span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t116" href="#t116">116</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t117" href="#t117">117</a></span><span class="t"><span class="str">        Initialization routine</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t118" href="#t118">118</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t119" href="#t119">119</a></span><span class="t"><span class="str">        Args:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t120" href="#t120">120</a></span><span class="t"><span class="str">            problem_params (dict): custom parameters for the example</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t121" href="#t121">121</a></span><span class="t"><span class="str">            dtype_u: mesh data type (will be passed parent class)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t122" href="#t122">122</a></span><span class="t"><span class="str">            dtype_f: mesh data type (will be passed parent class)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t123" href="#t123">123</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t124" href="#t124">124</a></span><span class="t">        <span class="com"># invoke super init, passing number of dofs, dtype_u and dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t125" href="#t125">125</a></span><span class="t">        <span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">__init__</span><span class="op">(</span><span class="nam">init</span><span class="op">=</span><span class="op">(</span><span class="nam">nvars</span><span class="op">,</span> <span class="key">None</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">dtype</span><span class="op">(</span><span class="str">'float64'</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t126" href="#t126">126</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">_makeAttributeAndRegister</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t127" href="#t127">127</a></span><span class="t">            <span class="str">'Cv'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t128" href="#t128">128</a></span><span class="t">            <span class="str">'K'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t129" href="#t129">129</a></span><span class="t">            <span class="str">'u_thresh'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t130" href="#t130">130</a></span><span class="t">            <span class="str">'u_max'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t131" href="#t131">131</a></span><span class="t">            <span class="str">'Q_max'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t132" href="#t132">132</a></span><span class="t">            <span class="str">'leak_range'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t133" href="#t133">133</a></span><span class="t">            <span class="str">'leak_type'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t134" href="#t134">134</a></span><span class="t">            <span class="str">'leak_transition'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t135" href="#t135">135</a></span><span class="t">            <span class="str">'order'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t136" href="#t136">136</a></span><span class="t">            <span class="str">'stencil_type'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t137" href="#t137">137</a></span><span class="t">            <span class="str">'bc'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t138" href="#t138">138</a></span><span class="t">            <span class="str">'nvars'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t139" href="#t139">139</a></span><span class="t">            <span class="str">'direct_solver'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t140" href="#t140">140</a></span><span class="t">            <span class="str">'reference_sol_type'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t141" href="#t141">141</a></span><span class="t">            <span class="nam">localVars</span><span class="op">=</span><span class="nam">locals</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t142" href="#t142">142</a></span><span class="t">            <span class="nam">readOnly</span><span class="op">=</span><span class="key">True</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t143" href="#t143">143</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t144" href="#t144">144</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">_makeAttributeAndRegister</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t145" href="#t145">145</a></span><span class="t">            <span class="str">'newton_tol'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t146" href="#t146">146</a></span><span class="t">            <span class="str">'newton_maxiter'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t147" href="#t147">147</a></span><span class="t">            <span class="str">'lintol'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t148" href="#t148">148</a></span><span class="t">            <span class="str">'liniter'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t149" href="#t149">149</a></span><span class="t">            <span class="str">'inexact_linear_ratio'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t150" href="#t150">150</a></span><span class="t">            <span class="str">'min_lintol'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t151" href="#t151">151</a></span><span class="t">            <span class="nam">localVars</span><span class="op">=</span><span class="nam">locals</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t152" href="#t152">152</a></span><span class="t">            <span class="nam">readOnly</span><span class="op">=</span><span class="key">False</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t153" href="#t153">153</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t154" href="#t154">154</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t155" href="#t155">155</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">_makeAttributeAndRegister</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t156" href="#t156">156</a></span><span class="t">            <span class="str">'newton_tol'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t157" href="#t157">157</a></span><span class="t">            <span class="str">'newton_maxiter'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t158" href="#t158">158</a></span><span class="t">            <span class="str">'lintol'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t159" href="#t159">159</a></span><span class="t">            <span class="str">'liniter'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t160" href="#t160">160</a></span><span class="t">            <span class="str">'direct_solver'</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t161" href="#t161">161</a></span><span class="t">            <span class="nam">localVars</span><span class="op">=</span><span class="nam">locals</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t162" href="#t162">162</a></span><span class="t">            <span class="nam">readOnly</span><span class="op">=</span><span class="key">False</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t163" href="#t163">163</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t164" href="#t164">164</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t165" href="#t165">165</a></span><span class="t">        <span class="com"># setup finite difference discretization from problem helper</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t166" href="#t166">166</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">dx</span><span class="op">,</span> <span class="nam">xvalues</span> <span class="op">=</span> <span class="nam">problem_helper</span><span class="op">.</span><span class="nam">get_1d_grid</span><span class="op">(</span><span class="nam">size</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">,</span> <span class="nam">bc</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">bc</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t167" href="#t167">167</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t168" href="#t168">168</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">b</span> <span class="op">=</span> <span class="nam">problem_helper</span><span class="op">.</span><span class="nam">get_finite_difference_matrix</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t169" href="#t169">169</a></span><span class="t">            <span class="nam">derivative</span><span class="op">=</span><span class="num">2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t170" href="#t170">170</a></span><span class="t">            <span class="nam">order</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">order</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t171" href="#t171">171</a></span><span class="t">            <span class="nam">stencil_type</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">stencil_type</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t172" href="#t172">172</a></span><span class="t">            <span class="nam">dx</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">dx</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t173" href="#t173">173</a></span><span class="t">            <span class="nam">size</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t174" href="#t174">174</a></span><span class="t">            <span class="nam">dim</span><span class="op">=</span><span class="num">1</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t175" href="#t175">175</a></span><span class="t">            <span class="nam">bc</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">bc</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t176" href="#t176">176</a></span><span class="t">        <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t177" href="#t177">177</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">A</span> <span class="op">*=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">K</span> <span class="op">/</span> <span class="nam">self</span><span class="op">.</span><span class="nam">Cv</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t178" href="#t178">178</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t179" href="#t179">179</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">xv</span> <span class="op">=</span> <span class="nam">xvalues</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t180" href="#t180">180</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">Id</span> <span class="op">=</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">eye</span><span class="op">(</span><span class="nam">np</span><span class="op">.</span><span class="nam">prod</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span><span class="op">,</span> <span class="nam">format</span><span class="op">=</span><span class="str">'csc'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t181" href="#t181">181</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t182" href="#t182">182</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">leak</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">logical_and</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">xv</span> <span class="op">></span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_range</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">xv</span> <span class="op">&lt;</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_range</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t183" href="#t183">183</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t184" href="#t184">184</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'newton'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">WorkCounter</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t185" href="#t185">185</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'rhs'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">WorkCounter</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t186" href="#t186">186</a></span><span class="t">        <span class="key">if</span> <span class="key">not</span> <span class="nam">self</span><span class="op">.</span><span class="nam">direct_solver</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t187" href="#t187">187</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'linear'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">WorkCounter</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t188" href="#t188">188</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t189" href="#t189">189</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f_non_linear</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t190" href="#t190">190</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t191" href="#t191">191</a></span><span class="t"><span class="str">        Get the non-linear part of f.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t192" href="#t192">192</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t193" href="#t193">193</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t194" href="#t194">194</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t195" href="#t195">195</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t196" href="#t196">196</a></span><span class="t"><span class="str">            Current values of the numerical solution:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t197" href="#t197">197</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t198" href="#t198">198</a></span><span class="t"><span class="str">            Current time at which the numerical solution is computed.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t199" href="#t199">199</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t200" href="#t200">200</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t201" href="#t201">201</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t202" href="#t202">202</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t203" href="#t203">203</a></span><span class="t"><span class="str">            The non-linear part of the right-hand side.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t204" href="#t204">204</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t205" href="#t205">205</a></span><span class="t">        <span class="nam">u_thresh</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">u_thresh</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t206" href="#t206">206</a></span><span class="t">        <span class="nam">u_max</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">u_max</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t207" href="#t207">207</a></span><span class="t">        <span class="nam">Q_max</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">Q_max</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t208" href="#t208">208</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t209" href="#t209">209</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t210" href="#t210">210</a></span><span class="t">        <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_type</span> <span class="op">==</span> <span class="str">'linear'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t211" href="#t211">211</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="op">(</span><span class="nam">u</span> <span class="op">-</span> <span class="nam">u_thresh</span><span class="op">)</span> <span class="op">/</span> <span class="op">(</span><span class="nam">u_max</span> <span class="op">-</span> <span class="nam">u_thresh</span><span class="op">)</span> <span class="op">*</span> <span class="nam">Q_max</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t212" href="#t212">212</a></span><span class="t">        <span class="key">elif</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_type</span> <span class="op">==</span> <span class="str">'exponential'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t213" href="#t213">213</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">Q_max</span> <span class="op">*</span> <span class="op">(</span><span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span> <span class="op">-</span> <span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u_thresh</span><span class="op">)</span><span class="op">)</span> <span class="op">/</span> <span class="op">(</span><span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u_max</span><span class="op">)</span> <span class="op">-</span> <span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u_thresh</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t214" href="#t214">214</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t215" href="#t215">215</a></span><span class="t">            <span class="key">raise</span> <span class="nam">NotImplementedError</span><span class="op">(</span><span class="str">f'Leak type \"{self.leak_type}\" not implemented!'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t216" href="#t216">216</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t217" href="#t217">217</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="nam">u</span> <span class="op">&lt;</span> <span class="nam">u_thresh</span><span class="op">]</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t218" href="#t218">218</a></span><span class="t">        <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_transition</span> <span class="op">==</span> <span class="str">'step'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t219" href="#t219">219</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">leak</span><span class="op">]</span> <span class="op">=</span> <span class="nam">Q_max</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t220" href="#t220">220</a></span><span class="t">        <span class="key">elif</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_transition</span> <span class="op">==</span> <span class="str">'Gaussian'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t221" href="#t221">221</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">max</span><span class="op">(</span><span class="op">[</span><span class="nam">me</span><span class="op">,</span> <span class="nam">Q_max</span> <span class="op">*</span> <span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="op">-</span><span class="op">(</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">xv</span> <span class="op">-</span> <span class="num">0.5</span><span class="op">)</span> <span class="op">**</span> <span class="num">2</span><span class="op">)</span> <span class="op">/</span> <span class="num">3e-2</span><span class="op">)</span><span class="op">]</span><span class="op">,</span> <span class="nam">axis</span><span class="op">=</span><span class="num">0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t222" href="#t222">222</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t223" href="#t223">223</a></span><span class="t">            <span class="key">raise</span> <span class="nam">NotImplementedError</span><span class="op">(</span><span class="str">f'Leak transition \"{self.leak_transition}\" not implemented!'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t224" href="#t224">224</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t225" href="#t225">225</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t226" href="#t226">226</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t227" href="#t227">227</a></span><span class="t"><span class="str">        Evaluate the full right-hand side.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t225" href="#t225">225</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="nam">u</span> <span class="op">>=</span> <span class="nam">u_max</span><span class="op">]</span> <span class="op">=</span> <span class="nam">Q_max</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t226" href="#t226">226</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t227" href="#t227">227</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">/=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">Cv</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t228" href="#t228">228</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t229" href="#t229">229</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t230" href="#t230">230</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t231" href="#t231">231</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t232" href="#t232">232</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t233" href="#t233">233</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t234" href="#t234">234</a></span><span class="t"><span class="str">            Current time at which the numerical solution is computed.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t235" href="#t235">235</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t236" href="#t236">236</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t237" href="#t237">237</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t238" href="#t238">238</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t239" href="#t239">239</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t240" href="#t240">240</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t241" href="#t241">241</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t242" href="#t242">242</a></span><span class="t">        <span class="nam">f</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">b</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eval_f_non_linear</span><span class="op">(</span><span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t243" href="#t243">243</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t244" href="#t244">244</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'rhs'</span><span class="op">]</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t245" href="#t245">245</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t246" href="#t246">246</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t247" href="#t247">247</a></span><span class="t">    <span class="key">def</span> <span class="nam">get_non_linear_Jacobian</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t248" href="#t248">248</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t249" href="#t249">249</a></span><span class="t"><span class="str">        Evaluate the non-linear part of the Jacobian only.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t250" href="#t250">250</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t251" href="#t251">251</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t252" href="#t252">252</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t253" href="#t253">253</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t254" href="#t254">254</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t255" href="#t255">255</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t256" href="#t256">256</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t257" href="#t257">257</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t258" href="#t258">258</a></span><span class="t"><span class="str">        scipy.sparse.csc</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t259" href="#t259">259</a></span><span class="t"><span class="str">            The derivative of the non-linear part of the solution w.r.t. to the solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t260" href="#t260">260</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t261" href="#t261">261</a></span><span class="t">        <span class="nam">u_thresh</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">u_thresh</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t262" href="#t262">262</a></span><span class="t">        <span class="nam">u_max</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">u_max</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t263" href="#t263">263</a></span><span class="t">        <span class="nam">Q_max</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">Q_max</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t264" href="#t264">264</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t265" href="#t265">265</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t266" href="#t266">266</a></span><span class="t">        <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_type</span> <span class="op">==</span> <span class="str">'linear'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t267" href="#t267">267</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">Q_max</span> <span class="op">/</span> <span class="op">(</span><span class="nam">u_max</span> <span class="op">-</span> <span class="nam">u_thresh</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t268" href="#t268">268</a></span><span class="t">        <span class="key">elif</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_type</span> <span class="op">==</span> <span class="str">'exponential'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t269" href="#t269">269</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">Q_max</span> <span class="op">*</span> <span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span> <span class="op">/</span> <span class="op">(</span><span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u_max</span><span class="op">)</span> <span class="op">-</span> <span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u_thresh</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t270" href="#t270">270</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t271" href="#t271">271</a></span><span class="t">            <span class="key">raise</span> <span class="nam">NotImplementedError</span><span class="op">(</span><span class="str">f'Leak type {self.leak_type} not implemented!'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t272" href="#t272">272</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t273" href="#t273">273</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="nam">u</span> <span class="op">&lt;</span> <span class="nam">u_thresh</span><span class="op">]</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t274" href="#t274">274</a></span><span class="t">        <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_transition</span> <span class="op">==</span> <span class="str">'step'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t275" href="#t275">275</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">leak</span><span class="op">]</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t276" href="#t276">276</a></span><span class="t">        <span class="key">elif</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_transition</span> <span class="op">==</span> <span class="str">'Gaussian'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t277" href="#t277">277</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">leak</span><span class="op">]</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t278" href="#t278">278</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">leak</span><span class="op">]</span><span class="op">[</span><span class="nam">u</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">leak</span><span class="op">]</span> <span class="op">></span> <span class="nam">Q_max</span> <span class="op">*</span> <span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="op">-</span><span class="op">(</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">xv</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">leak</span><span class="op">]</span> <span class="op">-</span> <span class="num">0.5</span><span class="op">)</span> <span class="op">**</span> <span class="num">2</span><span class="op">)</span> <span class="op">/</span> <span class="num">3e-2</span><span class="op">)</span><span class="op">]</span> <span class="op">=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t279" href="#t279">279</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t280" href="#t280">280</a></span><span class="t">            <span class="key">raise</span> <span class="nam">NotImplementedError</span><span class="op">(</span><span class="str">f'Leak transition \"{self.leak_transition}\" not implemented!'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t281" href="#t281">281</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="nam">u</span> <span class="op">></span> <span class="nam">u_max</span><span class="op">]</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t282" href="#t282">282</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t283" href="#t283">283</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">/=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">Cv</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t284" href="#t284">284</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t285" href="#t285">285</a></span><span class="t">        <span class="key">return</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">diags</span><span class="op">(</span><span class="nam">me</span><span class="op">,</span> <span class="nam">format</span><span class="op">=</span><span class="str">'csc'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t286" href="#t286">286</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t287" href="#t287">287</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t288" href="#t288">288</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t289" href="#t289">289</a></span><span class="t"><span class="str">        Simple Newton solver for :math:`(I - factor \cdot f)(\vec{u}) = \vec{rhs}`.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t229" href="#t229">229</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t230" href="#t230">230</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t231" href="#t231">231</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t232" href="#t232">232</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t233" href="#t233">233</a></span><span class="t"><span class="str">        Evaluate the full right-hand side.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t234" href="#t234">234</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t235" href="#t235">235</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t236" href="#t236">236</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t237" href="#t237">237</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t238" href="#t238">238</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t239" href="#t239">239</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t240" href="#t240">240</a></span><span class="t"><span class="str">            Current time at which the numerical solution is computed.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t241" href="#t241">241</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t242" href="#t242">242</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t243" href="#t243">243</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t244" href="#t244">244</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t245" href="#t245">245</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t246" href="#t246">246</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t247" href="#t247">247</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t248" href="#t248">248</a></span><span class="t">        <span class="nam">f</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">b</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eval_f_non_linear</span><span class="op">(</span><span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t249" href="#t249">249</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t250" href="#t250">250</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'rhs'</span><span class="op">]</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t251" href="#t251">251</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t252" href="#t252">252</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t253" href="#t253">253</a></span><span class="t">    <span class="key">def</span> <span class="nam">get_non_linear_Jacobian</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t254" href="#t254">254</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t255" href="#t255">255</a></span><span class="t"><span class="str">        Evaluate the non-linear part of the Jacobian only.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t256" href="#t256">256</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t257" href="#t257">257</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t258" href="#t258">258</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t259" href="#t259">259</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t260" href="#t260">260</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t261" href="#t261">261</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t262" href="#t262">262</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t263" href="#t263">263</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t264" href="#t264">264</a></span><span class="t"><span class="str">        scipy.sparse.csc</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t265" href="#t265">265</a></span><span class="t"><span class="str">            The derivative of the non-linear part of the solution w.r.t. to the solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t266" href="#t266">266</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t267" href="#t267">267</a></span><span class="t">        <span class="nam">u_thresh</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">u_thresh</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t268" href="#t268">268</a></span><span class="t">        <span class="nam">u_max</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">u_max</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t269" href="#t269">269</a></span><span class="t">        <span class="nam">Q_max</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">Q_max</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t270" href="#t270">270</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t271" href="#t271">271</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t272" href="#t272">272</a></span><span class="t">        <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_type</span> <span class="op">==</span> <span class="str">'linear'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t273" href="#t273">273</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">Q_max</span> <span class="op">/</span> <span class="op">(</span><span class="nam">u_max</span> <span class="op">-</span> <span class="nam">u_thresh</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t274" href="#t274">274</a></span><span class="t">        <span class="key">elif</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_type</span> <span class="op">==</span> <span class="str">'exponential'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t275" href="#t275">275</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">Q_max</span> <span class="op">*</span> <span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span> <span class="op">/</span> <span class="op">(</span><span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u_max</span><span class="op">)</span> <span class="op">-</span> <span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="nam">u_thresh</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t276" href="#t276">276</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t277" href="#t277">277</a></span><span class="t">            <span class="key">raise</span> <span class="nam">NotImplementedError</span><span class="op">(</span><span class="str">f'Leak type {self.leak_type} not implemented!'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t278" href="#t278">278</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t279" href="#t279">279</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="nam">u</span> <span class="op">&lt;</span> <span class="nam">u_thresh</span><span class="op">]</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t280" href="#t280">280</a></span><span class="t">        <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_transition</span> <span class="op">==</span> <span class="str">'step'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t281" href="#t281">281</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">leak</span><span class="op">]</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t282" href="#t282">282</a></span><span class="t">        <span class="key">elif</span> <span class="nam">self</span><span class="op">.</span><span class="nam">leak_transition</span> <span class="op">==</span> <span class="str">'Gaussian'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t283" href="#t283">283</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">leak</span><span class="op">]</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t284" href="#t284">284</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">leak</span><span class="op">]</span><span class="op">[</span><span class="nam">u</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">leak</span><span class="op">]</span> <span class="op">></span> <span class="nam">Q_max</span> <span class="op">*</span> <span class="nam">np</span><span class="op">.</span><span class="nam">exp</span><span class="op">(</span><span class="op">-</span><span class="op">(</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">xv</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">leak</span><span class="op">]</span> <span class="op">-</span> <span class="num">0.5</span><span class="op">)</span> <span class="op">**</span> <span class="num">2</span><span class="op">)</span> <span class="op">/</span> <span class="num">3e-2</span><span class="op">)</span><span class="op">]</span> <span class="op">=</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t285" href="#t285">285</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t286" href="#t286">286</a></span><span class="t">            <span class="key">raise</span> <span class="nam">NotImplementedError</span><span class="op">(</span><span class="str">f'Leak transition \"{self.leak_transition}\" not implemented!'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t287" href="#t287">287</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="nam">u</span> <span class="op">></span> <span class="nam">u_max</span><span class="op">]</span> <span class="op">=</span> <span class="num">0</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t288" href="#t288">288</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t289" href="#t289">289</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">/=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">Cv</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t290" href="#t290">290</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t291" href="#t291">291</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t292" href="#t292">292</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t293" href="#t293">293</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t294" href="#t294">294</a></span><span class="t"><span class="str">            Right-hand side.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t295" href="#t295">295</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t296" href="#t296">296</a></span><span class="t"><span class="str">            Abbrev. for the local stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t297" href="#t297">297</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t298" href="#t298">298</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t299" href="#t299">299</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t300" href="#t300">300</a></span><span class="t"><span class="str">            Current time (e.g. for time-dependent BCs).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t301" href="#t301">301</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t302" href="#t302">302</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t303" href="#t303">303</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t304" href="#t304">304</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t305" href="#t305">305</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t306" href="#t306">306</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t307" href="#t307">307</a></span><span class="t">        <span class="nam">u</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">u0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t308" href="#t308">308</a></span><span class="t">        <span class="nam">res</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">inf</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t309" href="#t309">309</a></span><span class="t">        <span class="nam">delta</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t310" href="#t310">310</a></span><span class="t">        <span class="nam">z</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t311" href="#t311">311</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t312" href="#t312">312</a></span><span class="t">        <span class="com"># construct a preconditioner for the space solver</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t313" href="#t313">313</a></span><span class="t">        <span class="key">if</span> <span class="key">not</span> <span class="nam">self</span><span class="op">.</span><span class="nam">direct_solver</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t314" href="#t314">314</a></span><span class="t">            <span class="nam">M</span> <span class="op">=</span> <span class="nam">inv</span><span class="op">(</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">)</span><span class="op">.</span><span class="nam">toarray</span><span class="op">(</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t315" href="#t315">315</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t316" href="#t316">316</a></span><span class="t">        <span class="key">for</span> <span class="nam">n</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="num">0</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_maxiter</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t317" href="#t317">317</a></span><span class="t">            <span class="com"># assemble G such that G(u) = 0 at the solution of the step</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t318" href="#t318">318</a></span><span class="t">            <span class="nam">G</span> <span class="op">=</span> <span class="nam">u</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eval_f</span><span class="op">(</span><span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span> <span class="op">-</span> <span class="nam">rhs</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t319" href="#t319">319</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t320" href="#t320">320</a></span><span class="t">                <span class="str">'rhs'</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t321" href="#t321">321</a></span><span class="t">            <span class="op">]</span><span class="op">.</span><span class="nam">decrement</span><span class="op">(</span><span class="op">)</span>  <span class="com"># Work regarding construction of the Jacobian etc. should count into the Newton iterations only</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t322" href="#t322">322</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t323" href="#t323">323</a></span><span class="t">            <span class="nam">res</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">linalg</span><span class="op">.</span><span class="nam">norm</span><span class="op">(</span><span class="nam">G</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">inf</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t324" href="#t324">324</a></span><span class="t">            <span class="key">if</span> <span class="nam">res</span> <span class="op">&lt;=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_tol</span> <span class="key">and</span> <span class="nam">n</span> <span class="op">></span> <span class="num">0</span><span class="op">:</span>  <span class="com"># we want to make at least one Newton iteration</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t325" href="#t325">325</a></span><span class="t">                <span class="key">break</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t326" href="#t326">326</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t327" href="#t327">327</a></span><span class="t">            <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">inexact_linear_ratio</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t328" href="#t328">328</a></span><span class="t">                <span class="nam">self</span><span class="op">.</span><span class="nam">lintol</span> <span class="op">=</span> <span class="nam">max</span><span class="op">(</span><span class="op">[</span><span class="nam">res</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">inexact_linear_ratio</span><span class="op">,</span> <span class="num">1e-12</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t329" href="#t329">329</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t330" href="#t330">330</a></span><span class="t">            <span class="com"># assemble Jacobian J of G</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t331" href="#t331">331</a></span><span class="t">            <span class="nam">J</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">get_non_linear_Jacobian</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t291" href="#t291">291</a></span><span class="t">        <span class="key">return</span> <span class="nam">sp</span><span class="op">.</span><span class="nam">diags</span><span class="op">(</span><span class="nam">me</span><span class="op">,</span> <span class="nam">format</span><span class="op">=</span><span class="str">'csc'</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t292" href="#t292">292</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t293" href="#t293">293</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t294" href="#t294">294</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t295" href="#t295">295</a></span><span class="t"><span class="str">        Simple Newton solver for :math:`(I - factor \cdot f)(\vec{u}) = \vec{rhs}`.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t296" href="#t296">296</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t297" href="#t297">297</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t298" href="#t298">298</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t299" href="#t299">299</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t300" href="#t300">300</a></span><span class="t"><span class="str">            Right-hand side.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t301" href="#t301">301</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t302" href="#t302">302</a></span><span class="t"><span class="str">            Abbrev. for the local stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t303" href="#t303">303</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t304" href="#t304">304</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t305" href="#t305">305</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t306" href="#t306">306</a></span><span class="t"><span class="str">            Current time (e.g. for time-dependent BCs).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t307" href="#t307">307</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t308" href="#t308">308</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t309" href="#t309">309</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t310" href="#t310">310</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t311" href="#t311">311</a></span><span class="t"><span class="str">            The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t312" href="#t312">312</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t313" href="#t313">313</a></span><span class="t">        <span class="nam">u</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">u0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t314" href="#t314">314</a></span><span class="t">        <span class="nam">res</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">inf</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t315" href="#t315">315</a></span><span class="t">        <span class="nam">delta</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t316" href="#t316">316</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t317" href="#t317">317</a></span><span class="t">        <span class="com"># construct a preconditioner for the space solver</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t318" href="#t318">318</a></span><span class="t">        <span class="key">if</span> <span class="key">not</span> <span class="nam">self</span><span class="op">.</span><span class="nam">direct_solver</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t319" href="#t319">319</a></span><span class="t">            <span class="nam">M</span> <span class="op">=</span> <span class="nam">inv</span><span class="op">(</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">)</span><span class="op">.</span><span class="nam">toarray</span><span class="op">(</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t320" href="#t320">320</a></span><span class="t">            <span class="nam">zero</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t321" href="#t321">321</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t322" href="#t322">322</a></span><span class="t">        <span class="key">for</span> <span class="nam">n</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="num">0</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_maxiter</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t323" href="#t323">323</a></span><span class="t">            <span class="com"># assemble G such that G(u) = 0 at the solution of the step</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t324" href="#t324">324</a></span><span class="t">            <span class="nam">G</span> <span class="op">=</span> <span class="nam">u</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eval_f</span><span class="op">(</span><span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span> <span class="op">-</span> <span class="nam">rhs</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t325" href="#t325">325</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t326" href="#t326">326</a></span><span class="t">                <span class="str">'rhs'</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t327" href="#t327">327</a></span><span class="t">            <span class="op">]</span><span class="op">.</span><span class="nam">decrement</span><span class="op">(</span><span class="op">)</span>  <span class="com"># Work regarding construction of the Jacobian etc. should count into the Newton iterations only</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t328" href="#t328">328</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t329" href="#t329">329</a></span><span class="t">            <span class="nam">res</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">linalg</span><span class="op">.</span><span class="nam">norm</span><span class="op">(</span><span class="nam">G</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">inf</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t330" href="#t330">330</a></span><span class="t">            <span class="key">if</span> <span class="nam">res</span> <span class="op">&lt;=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">newton_tol</span> <span class="key">and</span> <span class="nam">n</span> <span class="op">></span> <span class="num">0</span><span class="op">:</span>  <span class="com"># we want to make at least one Newton iteration</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t331" href="#t331">331</a></span><span class="t">                <span class="key">break</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t332" href="#t332">332</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t333" href="#t333">333</a></span><span class="t">            <span class="com"># solve the linear system</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t334" href="#t334">334</a></span><span class="t">            <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">direct_solver</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t335" href="#t335">335</a></span><span class="t">                <span class="nam">delta</span> <span class="op">=</span> <span class="nam">spsolve</span><span class="op">(</span><span class="nam">J</span><span class="op">,</span> <span class="nam">G</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t336" href="#t336">336</a></span><span class="t">            <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t337" href="#t337">337</a></span><span class="t">                <span class="nam">delta</span><span class="op">,</span> <span class="nam">info</span> <span class="op">=</span> <span class="nam">gmres</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t338" href="#t338">338</a></span><span class="t">                    <span class="nam">J</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t339" href="#t339">339</a></span><span class="t">                    <span class="nam">G</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t340" href="#t340">340</a></span><span class="t">                    <span class="nam">x0</span><span class="op">=</span><span class="nam">z</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t341" href="#t341">341</a></span><span class="t">                    <span class="nam">M</span><span class="op">=</span><span class="nam">M</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t342" href="#t342">342</a></span><span class="t">                    <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lintol</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t343" href="#t343">343</a></span><span class="t">                    <span class="nam">maxiter</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">liniter</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t344" href="#t344">344</a></span><span class="t">                    <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t345" href="#t345">345</a></span><span class="t">                    <span class="nam">callback</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'linear'</span><span class="op">]</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t346" href="#t346">346</a></span><span class="t">                <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t347" href="#t347">347</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t348" href="#t348">348</a></span><span class="t">            <span class="key">if</span> <span class="key">not</span> <span class="nam">np</span><span class="op">.</span><span class="nam">isfinite</span><span class="op">(</span><span class="nam">delta</span><span class="op">)</span><span class="op">.</span><span class="nam">all</span><span class="op">(</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t349" href="#t349">349</a></span><span class="t">                <span class="key">break</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t350" href="#t350">350</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t351" href="#t351">351</a></span><span class="t">            <span class="com"># update solution</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t352" href="#t352">352</a></span><span class="t">            <span class="nam">u</span> <span class="op">=</span> <span class="nam">u</span> <span class="op">-</span> <span class="nam">delta</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t333" href="#t333">333</a></span><span class="t">            <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">inexact_linear_ratio</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t334" href="#t334">334</a></span><span class="t">                <span class="nam">self</span><span class="op">.</span><span class="nam">lintol</span> <span class="op">=</span> <span class="nam">max</span><span class="op">(</span><span class="op">[</span><span class="nam">res</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">inexact_linear_ratio</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">min_lintol</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t335" href="#t335">335</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t336" href="#t336">336</a></span><span class="t">            <span class="com"># assemble Jacobian J of G</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t337" href="#t337">337</a></span><span class="t">            <span class="nam">J</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">A</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">get_non_linear_Jacobian</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t338" href="#t338">338</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t339" href="#t339">339</a></span><span class="t">            <span class="com"># solve the linear system</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t340" href="#t340">340</a></span><span class="t">            <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">direct_solver</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t341" href="#t341">341</a></span><span class="t">                <span class="nam">delta</span> <span class="op">=</span> <span class="nam">spsolve</span><span class="op">(</span><span class="nam">J</span><span class="op">,</span> <span class="nam">G</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t342" href="#t342">342</a></span><span class="t">            <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t343" href="#t343">343</a></span><span class="t">                <span class="nam">delta</span><span class="op">,</span> <span class="nam">info</span> <span class="op">=</span> <span class="nam">gmres</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t344" href="#t344">344</a></span><span class="t">                    <span class="nam">J</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t345" href="#t345">345</a></span><span class="t">                    <span class="nam">G</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t346" href="#t346">346</a></span><span class="t">                    <span class="nam">x0</span><span class="op">=</span><span class="nam">zero</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t347" href="#t347">347</a></span><span class="t">                    <span class="nam">M</span><span class="op">=</span><span class="nam">M</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t348" href="#t348">348</a></span><span class="t">                    <span class="nam">tol</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">lintol</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t349" href="#t349">349</a></span><span class="t">                    <span class="nam">maxiter</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">liniter</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t350" href="#t350">350</a></span><span class="t">                    <span class="nam">atol</span><span class="op">=</span><span class="num">0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t351" href="#t351">351</a></span><span class="t">                    <span class="nam">callback</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'linear'</span><span class="op">]</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t352" href="#t352">352</a></span><span class="t">                <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t353" href="#t353">353</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t354" href="#t354">354</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'newton'</span><span class="op">]</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t355" href="#t355">355</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t356" href="#t356">356</a></span><span class="t">        <span class="key">return</span> <span class="nam">u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t357" href="#t357">357</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t358" href="#t358">358</a></span><span class="t">    <span class="key">def</span> <span class="nam">u_exact</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">=</span><span class="key">None</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">=</span><span class="key">None</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t359" href="#t359">359</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t360" href="#t360">360</a></span><span class="t"><span class="str">        Routine to compute the exact solution at time :math:`t`.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t354" href="#t354">354</a></span><span class="t">            <span class="key">if</span> <span class="key">not</span> <span class="nam">np</span><span class="op">.</span><span class="nam">isfinite</span><span class="op">(</span><span class="nam">delta</span><span class="op">)</span><span class="op">.</span><span class="nam">all</span><span class="op">(</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t355" href="#t355">355</a></span><span class="t">                <span class="key">break</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t356" href="#t356">356</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t357" href="#t357">357</a></span><span class="t">            <span class="com"># update solution</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t358" href="#t358">358</a></span><span class="t">            <span class="nam">u</span> <span class="op">=</span> <span class="nam">u</span> <span class="op">-</span> <span class="nam">delta</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t359" href="#t359">359</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t360" href="#t360">360</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'newton'</span><span class="op">]</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t361" href="#t361">361</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t362" href="#t362">362</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t363" href="#t363">363</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t364" href="#t364">364</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t365" href="#t365">365</a></span><span class="t"><span class="str">            Time of the exact solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t366" href="#t366">366</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t367" href="#t367">367</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t368" href="#t368">368</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t369" href="#t369">369</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t370" href="#t370">370</a></span><span class="t"><span class="str">            The exact solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t371" href="#t371">371</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t362" href="#t362">362</a></span><span class="t">        <span class="key">return</span> <span class="nam">u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t363" href="#t363">363</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t364" href="#t364">364</a></span><span class="t">    <span class="key">def</span> <span class="nam">u_exact</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">=</span><span class="key">None</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">=</span><span class="key">None</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t365" href="#t365">365</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t366" href="#t366">366</a></span><span class="t"><span class="str">        Routine to compute the exact solution at time :math:`t`.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t367" href="#t367">367</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t368" href="#t368">368</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t369" href="#t369">369</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t370" href="#t370">370</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t371" href="#t371">371</a></span><span class="t"><span class="str">            Time of the exact solution.</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t372" href="#t372">372</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t373" href="#t373">373</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t374" href="#t374">374</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t375" href="#t375">375</a></span><span class="t">        <span class="key">if</span> <span class="nam">t</span> <span class="op">></span> <span class="num">0</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t376" href="#t376">376</a></span><span class="t">            <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">reference_sol_type</span> <span class="op">==</span> <span class="str">'scipy'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t377" href="#t377">377</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t378" href="#t378">378</a></span><span class="t">                <span class="key">def</span> <span class="nam">jac</span><span class="op">(</span><span class="nam">t</span><span class="op">,</span> <span class="nam">u</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t379" href="#t379">379</a></span><span class="t">                    <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t380" href="#t380">380</a></span><span class="t"><span class="str">                    Get the Jacobian for the implicit BDF method to use in `scipy.solve_ivp`</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t381" href="#t381">381</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t382" href="#t382">382</a></span><span class="t"><span class="str">                    Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t383" href="#t383">383</a></span><span class="t"><span class="str">                    ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t384" href="#t384">384</a></span><span class="t"><span class="str">                    t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t385" href="#t385">385</a></span><span class="t"><span class="str">                        The current time.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t386" href="#t386">386</a></span><span class="t"><span class="str">                    u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t387" href="#t387">387</a></span><span class="t"><span class="str">                        Current solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t388" href="#t388">388</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t389" href="#t389">389</a></span><span class="t"><span class="str">                    Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t390" href="#t390">390</a></span><span class="t"><span class="str">                    -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t391" href="#t391">391</a></span><span class="t"><span class="str">                    scipy.sparse.csc</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t392" href="#t392">392</a></span><span class="t"><span class="str">                        The derivative of the non-linear part of the solution w.r.t. to the solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t393" href="#t393">393</a></span><span class="t"><span class="str">                    """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t394" href="#t394">394</a></span><span class="t">                    <span class="key">return</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">get_non_linear_Jacobian</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t395" href="#t395">395</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t396" href="#t396">396</a></span><span class="t">                <span class="key">def</span> <span class="nam">eval_rhs</span><span class="op">(</span><span class="nam">t</span><span class="op">,</span> <span class="nam">u</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t397" href="#t397">397</a></span><span class="t">                    <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t398" href="#t398">398</a></span><span class="t"><span class="str">                    Function to pass to `scipy.solve_ivp` to evaluate the full right-hand side.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t399" href="#t399">399</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t400" href="#t400">400</a></span><span class="t"><span class="str">                    Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t401" href="#t401">401</a></span><span class="t"><span class="str">                    ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t402" href="#t402">402</a></span><span class="t"><span class="str">                    t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t403" href="#t403">403</a></span><span class="t"><span class="str">                        Current time.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t404" href="#t404">404</a></span><span class="t"><span class="str">                    u : numpy.1darray</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t405" href="#t405">405</a></span><span class="t"><span class="str">                        Current solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t406" href="#t406">406</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t407" href="#t407">407</a></span><span class="t"><span class="str">                    Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t408" href="#t408">408</a></span><span class="t"><span class="str">                    -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t409" href="#t409">409</a></span><span class="t"><span class="str">                    numpy.1darray</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t410" href="#t410">410</a></span><span class="t"><span class="str">                        Right-hand side.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t411" href="#t411">411</a></span><span class="t"><span class="str">                    """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t412" href="#t412">412</a></span><span class="t">                    <span class="key">return</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eval_f</span><span class="op">(</span><span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t413" href="#t413">413</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t414" href="#t414">414</a></span><span class="t">                <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">generate_scipy_reference_solution</span><span class="op">(</span><span class="nam">eval_rhs</span><span class="op">,</span> <span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">,</span> <span class="nam">method</span><span class="op">=</span><span class="str">'BDF'</span><span class="op">,</span> <span class="nam">jac</span><span class="op">=</span><span class="nam">jac</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t415" href="#t415">415</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t416" href="#t416">416</a></span><span class="t">            <span class="key">elif</span> <span class="nam">self</span><span class="op">.</span><span class="nam">reference_sol_type</span> <span class="key">in</span> <span class="op">[</span><span class="str">'DIRK'</span><span class="op">,</span> <span class="str">'SDC'</span><span class="op">]</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t417" href="#t417">417</a></span><span class="t">                <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">controller_classes</span><span class="op">.</span><span class="nam">controller_nonMPI</span> <span class="key">import</span> <span class="nam">controller_nonMPI</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t418" href="#t418">418</a></span><span class="t">                <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">hooks</span><span class="op">.</span><span class="nam">log_solution</span> <span class="key">import</span> <span class="nam">LogSolution</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t419" href="#t419">419</a></span><span class="t">                <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">helpers</span><span class="op">.</span><span class="nam">stats_helper</span> <span class="key">import</span> <span class="nam">get_sorted</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t420" href="#t420">420</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t421" href="#t421">421</a></span><span class="t">                <span class="nam">description</span> <span class="op">=</span> <span class="op">{</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t422" href="#t422">422</a></span><span class="t">                <span class="nam">description</span><span class="op">[</span><span class="str">'problem_class'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">Quench</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t423" href="#t423">423</a></span><span class="t">                <span class="nam">description</span><span class="op">[</span><span class="str">'problem_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t424" href="#t424">424</a></span><span class="t">                    <span class="str">'newton_tol'</span><span class="op">:</span> <span class="num">1e-10</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t425" href="#t425">425</a></span><span class="t">                    <span class="str">'newton_maxiter'</span><span class="op">:</span> <span class="num">99</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t426" href="#t426">426</a></span><span class="t">                    <span class="str">'nvars'</span><span class="op">:</span> <span class="num">2</span><span class="op">**</span><span class="num">10</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t427" href="#t427">427</a></span><span class="t">                    <span class="op">**</span><span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t428" href="#t428">428</a></span><span class="t">                <span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t429" href="#t429">429</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t430" href="#t430">430</a></span><span class="t">                <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">reference_sol_type</span> <span class="op">==</span> <span class="str">'DIRK'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t431" href="#t431">431</a></span><span class="t">                    <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">sweeper_classes</span><span class="op">.</span><span class="nam">Runge_Kutta</span> <span class="key">import</span> <span class="nam">DIRK43</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t432" href="#t432">432</a></span><span class="t">                    <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">convergence_controller_classes</span><span class="op">.</span><span class="nam">adaptivity</span> <span class="key">import</span> <span class="nam">AdaptivityRK</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t433" href="#t433">433</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t434" href="#t434">434</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'sweeper_class'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">DIRK43</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t435" href="#t435">435</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'sweeper_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t436" href="#t436">436</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'step_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'maxiter'</span><span class="op">:</span> <span class="num">1</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t437" href="#t437">437</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'level_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'dt'</span><span class="op">:</span> <span class="num">1e-4</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t438" href="#t438">438</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'convergence_controllers'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="nam">AdaptivityRK</span><span class="op">:</span> <span class="op">{</span><span class="str">'e_tol'</span><span class="op">:</span> <span class="num">1e-9</span><span class="op">,</span> <span class="str">'update_order'</span><span class="op">:</span> <span class="num">4</span><span class="op">}</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t439" href="#t439">439</a></span><span class="t">                <span class="key">elif</span> <span class="nam">self</span><span class="op">.</span><span class="nam">reference_sol_type</span> <span class="op">==</span> <span class="str">'SDC'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t440" href="#t440">440</a></span><span class="t">                    <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">sweeper_classes</span><span class="op">.</span><span class="nam">generic_implicit</span> <span class="key">import</span> <span class="nam">generic_implicit</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t441" href="#t441">441</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t442" href="#t442">442</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'sweeper_class'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">generic_implicit</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t443" href="#t443">443</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'sweeper_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'num_nodes'</span><span class="op">:</span> <span class="num">3</span><span class="op">,</span> <span class="str">'QI'</span><span class="op">:</span> <span class="str">'IE'</span><span class="op">,</span> <span class="str">'quad_type'</span><span class="op">:</span> <span class="str">'RADAU-RIGHT'</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t444" href="#t444">444</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'step_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'maxiter'</span><span class="op">:</span> <span class="num">99</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t445" href="#t445">445</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'level_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'dt'</span><span class="op">:</span> <span class="num">0.5</span><span class="op">,</span> <span class="str">'restol'</span><span class="op">:</span> <span class="num">1e-10</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t446" href="#t446">446</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t447" href="#t447">447</a></span><span class="t">                <span class="nam">controller_params</span> <span class="op">=</span> <span class="op">{</span><span class="str">'hook_class'</span><span class="op">:</span> <span class="nam">LogSolution</span><span class="op">,</span> <span class="str">'mssdc_jac'</span><span class="op">:</span> <span class="key">False</span><span class="op">,</span> <span class="str">'logger_level'</span><span class="op">:</span> <span class="num">99</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t448" href="#t448">448</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t449" href="#t449">449</a></span><span class="t">                <span class="nam">controller</span> <span class="op">=</span> <span class="nam">controller_nonMPI</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t450" href="#t450">450</a></span><span class="t">                    <span class="nam">description</span><span class="op">=</span><span class="nam">description</span><span class="op">,</span> <span class="nam">controller_params</span><span class="op">=</span><span class="nam">controller_params</span><span class="op">,</span> <span class="nam">num_procs</span><span class="op">=</span><span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t451" href="#t451">451</a></span><span class="t">                <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t373" href="#t373">373</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t374" href="#t374">374</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t375" href="#t375">375</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t376" href="#t376">376</a></span><span class="t"><span class="str">            The exact solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t377" href="#t377">377</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t378" href="#t378">378</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t379" href="#t379">379</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t380" href="#t380">380</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t381" href="#t381">381</a></span><span class="t">        <span class="key">if</span> <span class="nam">t</span> <span class="op">></span> <span class="num">0</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t382" href="#t382">382</a></span><span class="t">            <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">reference_sol_type</span> <span class="op">==</span> <span class="str">'scipy'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t383" href="#t383">383</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t384" href="#t384">384</a></span><span class="t">                <span class="key">def</span> <span class="nam">jac</span><span class="op">(</span><span class="nam">t</span><span class="op">,</span> <span class="nam">u</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t385" href="#t385">385</a></span><span class="t">                    <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t386" href="#t386">386</a></span><span class="t"><span class="str">                    Get the Jacobian for the implicit BDF method to use in `scipy.solve_ivp`</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t387" href="#t387">387</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t388" href="#t388">388</a></span><span class="t"><span class="str">                    Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t389" href="#t389">389</a></span><span class="t"><span class="str">                    ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t390" href="#t390">390</a></span><span class="t"><span class="str">                    t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t391" href="#t391">391</a></span><span class="t"><span class="str">                        The current time.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t392" href="#t392">392</a></span><span class="t"><span class="str">                    u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t393" href="#t393">393</a></span><span class="t"><span class="str">                        Current solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t394" href="#t394">394</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t395" href="#t395">395</a></span><span class="t"><span class="str">                    Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t396" href="#t396">396</a></span><span class="t"><span class="str">                    -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t397" href="#t397">397</a></span><span class="t"><span class="str">                    scipy.sparse.csc</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t398" href="#t398">398</a></span><span class="t"><span class="str">                        The derivative of the non-linear part of the solution w.r.t. to the solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t399" href="#t399">399</a></span><span class="t"><span class="str">                    """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t400" href="#t400">400</a></span><span class="t">                    <span class="key">return</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">get_non_linear_Jacobian</span><span class="op">(</span><span class="nam">u</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t401" href="#t401">401</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t402" href="#t402">402</a></span><span class="t">                <span class="key">def</span> <span class="nam">eval_rhs</span><span class="op">(</span><span class="nam">t</span><span class="op">,</span> <span class="nam">u</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t403" href="#t403">403</a></span><span class="t">                    <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t404" href="#t404">404</a></span><span class="t"><span class="str">                    Function to pass to `scipy.solve_ivp` to evaluate the full right-hand side.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t405" href="#t405">405</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t406" href="#t406">406</a></span><span class="t"><span class="str">                    Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t407" href="#t407">407</a></span><span class="t"><span class="str">                    ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t408" href="#t408">408</a></span><span class="t"><span class="str">                    t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t409" href="#t409">409</a></span><span class="t"><span class="str">                        Current time.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t410" href="#t410">410</a></span><span class="t"><span class="str">                    u : numpy.1darray</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t411" href="#t411">411</a></span><span class="t"><span class="str">                        Current solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t412" href="#t412">412</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t413" href="#t413">413</a></span><span class="t"><span class="str">                    Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t414" href="#t414">414</a></span><span class="t"><span class="str">                    -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t415" href="#t415">415</a></span><span class="t"><span class="str">                    numpy.1darray</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t416" href="#t416">416</a></span><span class="t"><span class="str">                        Right-hand side.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t417" href="#t417">417</a></span><span class="t"><span class="str">                    """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t418" href="#t418">418</a></span><span class="t">                    <span class="key">return</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eval_f</span><span class="op">(</span><span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t419" href="#t419">419</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t420" href="#t420">420</a></span><span class="t">                <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">generate_scipy_reference_solution</span><span class="op">(</span><span class="nam">eval_rhs</span><span class="op">,</span> <span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">,</span> <span class="nam">method</span><span class="op">=</span><span class="str">'BDF'</span><span class="op">,</span> <span class="nam">jac</span><span class="op">=</span><span class="nam">jac</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t421" href="#t421">421</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t422" href="#t422">422</a></span><span class="t">            <span class="key">elif</span> <span class="nam">self</span><span class="op">.</span><span class="nam">reference_sol_type</span> <span class="key">in</span> <span class="op">[</span><span class="str">'DIRK'</span><span class="op">,</span> <span class="str">'SDC'</span><span class="op">]</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t423" href="#t423">423</a></span><span class="t">                <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">controller_classes</span><span class="op">.</span><span class="nam">controller_nonMPI</span> <span class="key">import</span> <span class="nam">controller_nonMPI</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t424" href="#t424">424</a></span><span class="t">                <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">hooks</span><span class="op">.</span><span class="nam">log_solution</span> <span class="key">import</span> <span class="nam">LogSolution</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t425" href="#t425">425</a></span><span class="t">                <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">helpers</span><span class="op">.</span><span class="nam">stats_helper</span> <span class="key">import</span> <span class="nam">get_sorted</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t426" href="#t426">426</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t427" href="#t427">427</a></span><span class="t">                <span class="nam">description</span> <span class="op">=</span> <span class="op">{</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t428" href="#t428">428</a></span><span class="t">                <span class="nam">description</span><span class="op">[</span><span class="str">'problem_class'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">Quench</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t429" href="#t429">429</a></span><span class="t">                <span class="nam">description</span><span class="op">[</span><span class="str">'problem_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t430" href="#t430">430</a></span><span class="t">                    <span class="str">'newton_tol'</span><span class="op">:</span> <span class="num">1e-10</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t431" href="#t431">431</a></span><span class="t">                    <span class="str">'newton_maxiter'</span><span class="op">:</span> <span class="num">99</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t432" href="#t432">432</a></span><span class="t">                    <span class="str">'nvars'</span><span class="op">:</span> <span class="num">2</span><span class="op">**</span><span class="num">10</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t433" href="#t433">433</a></span><span class="t">                    <span class="op">**</span><span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t434" href="#t434">434</a></span><span class="t">                <span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t435" href="#t435">435</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t436" href="#t436">436</a></span><span class="t">                <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">reference_sol_type</span> <span class="op">==</span> <span class="str">'DIRK'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t437" href="#t437">437</a></span><span class="t">                    <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">sweeper_classes</span><span class="op">.</span><span class="nam">Runge_Kutta</span> <span class="key">import</span> <span class="nam">DIRK43</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t438" href="#t438">438</a></span><span class="t">                    <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">convergence_controller_classes</span><span class="op">.</span><span class="nam">adaptivity</span> <span class="key">import</span> <span class="nam">AdaptivityRK</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t439" href="#t439">439</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t440" href="#t440">440</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'sweeper_class'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">DIRK43</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t441" href="#t441">441</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'sweeper_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t442" href="#t442">442</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'step_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'maxiter'</span><span class="op">:</span> <span class="num">1</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t443" href="#t443">443</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'level_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'dt'</span><span class="op">:</span> <span class="num">1e-4</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t444" href="#t444">444</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'convergence_controllers'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="nam">AdaptivityRK</span><span class="op">:</span> <span class="op">{</span><span class="str">'e_tol'</span><span class="op">:</span> <span class="num">1e-9</span><span class="op">,</span> <span class="str">'update_order'</span><span class="op">:</span> <span class="num">4</span><span class="op">}</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t445" href="#t445">445</a></span><span class="t">                <span class="key">elif</span> <span class="nam">self</span><span class="op">.</span><span class="nam">reference_sol_type</span> <span class="op">==</span> <span class="str">'SDC'</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t446" href="#t446">446</a></span><span class="t">                    <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">sweeper_classes</span><span class="op">.</span><span class="nam">generic_implicit</span> <span class="key">import</span> <span class="nam">generic_implicit</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t447" href="#t447">447</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t448" href="#t448">448</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'sweeper_class'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">generic_implicit</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t449" href="#t449">449</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'sweeper_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'num_nodes'</span><span class="op">:</span> <span class="num">3</span><span class="op">,</span> <span class="str">'QI'</span><span class="op">:</span> <span class="str">'IE'</span><span class="op">,</span> <span class="str">'quad_type'</span><span class="op">:</span> <span class="str">'RADAU-RIGHT'</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t450" href="#t450">450</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'step_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'maxiter'</span><span class="op">:</span> <span class="num">99</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t451" href="#t451">451</a></span><span class="t">                    <span class="nam">description</span><span class="op">[</span><span class="str">'level_params'</span><span class="op">]</span> <span class="op">=</span> <span class="op">{</span><span class="str">'dt'</span><span class="op">:</span> <span class="num">0.5</span><span class="op">,</span> <span class="str">'restol'</span><span class="op">:</span> <span class="num">1e-10</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t452" href="#t452">452</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t453" href="#t453">453</a></span><span class="t">                <span class="nam">uend</span><span class="op">,</span> <span class="nam">stats</span> <span class="op">=</span> <span class="nam">controller</span><span class="op">.</span><span class="nam">run</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t454" href="#t454">454</a></span><span class="t">                    <span class="nam">u0</span><span class="op">=</span><span class="nam">u_init</span> <span class="key">if</span> <span class="nam">u_init</span> <span class="key">is</span> <span class="key">not</span> <span class="key">None</span> <span class="key">else</span> <span class="nam">self</span><span class="op">.</span><span class="nam">u_exact</span><span class="op">(</span><span class="nam">t</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t455" href="#t455">455</a></span><span class="t">                    <span class="nam">t0</span><span class="op">=</span><span class="nam">t_init</span> <span class="key">if</span> <span class="nam">t_init</span> <span class="key">is</span> <span class="key">not</span> <span class="key">None</span> <span class="key">else</span> <span class="num">0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t456" href="#t456">456</a></span><span class="t">                    <span class="nam">Tend</span><span class="op">=</span><span class="nam">t</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t453" href="#t453">453</a></span><span class="t">                <span class="nam">controller_params</span> <span class="op">=</span> <span class="op">{</span><span class="str">'hook_class'</span><span class="op">:</span> <span class="nam">LogSolution</span><span class="op">,</span> <span class="str">'mssdc_jac'</span><span class="op">:</span> <span class="key">False</span><span class="op">,</span> <span class="str">'logger_level'</span><span class="op">:</span> <span class="num">99</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t454" href="#t454">454</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t455" href="#t455">455</a></span><span class="t">                <span class="nam">controller</span> <span class="op">=</span> <span class="nam">controller_nonMPI</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t456" href="#t456">456</a></span><span class="t">                    <span class="nam">description</span><span class="op">=</span><span class="nam">description</span><span class="op">,</span> <span class="nam">controller_params</span><span class="op">=</span><span class="nam">controller_params</span><span class="op">,</span> <span class="nam">num_procs</span><span class="op">=</span><span class="num">1</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t457" href="#t457">457</a></span><span class="t">                <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t458" href="#t458">458</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t459" href="#t459">459</a></span><span class="t">                <span class="nam">u_last</span> <span class="op">=</span> <span class="nam">get_sorted</span><span class="op">(</span><span class="nam">stats</span><span class="op">,</span> <span class="nam">type</span><span class="op">=</span><span class="str">'u'</span><span class="op">,</span> <span class="nam">recomputed</span><span class="op">=</span><span class="key">False</span><span class="op">)</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t460" href="#t460">460</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t461" href="#t461">461</a></span><span class="t">                <span class="key">if</span> <span class="nam">abs</span><span class="op">(</span><span class="nam">u_last</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">-</span> <span class="nam">t</span><span class="op">)</span> <span class="op">></span> <span class="num">1e-2</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t462" href="#t462">462</a></span><span class="t">                    <span class="nam">self</span><span class="op">.</span><span class="nam">logger</span><span class="op">.</span><span class="nam">warning</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t463" href="#t463">463</a></span><span class="t">                        <span class="str">f'Time difference between reference solution and requested time is {abs(u_last[0]-t):.2e}!'</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t464" href="#t464">464</a></span><span class="t">                    <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t465" href="#t465">465</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="mis show_mis"><span class="n"><a id="t466" href="#t466">466</a></span><span class="t">                <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">u_last</span><span class="op">[</span><span class="num">1</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t467" href="#t467">467</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t468" href="#t468">468</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t469" href="#t469">469</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t470" href="#t470">470</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t471" href="#t471">471</a></span><span class="t"><span class="key">class</span> <span class="nam">QuenchIMEX</span><span class="op">(</span><span class="nam">Quench</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t472" href="#t472">472</a></span><span class="t">    <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t473" href="#t473">473</a></span><span class="t"><span class="str">    This is a toy problem [1]_ to emulate a magnet that has been cooled to temperatures where superconductivity is possible.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t474" href="#t474">474</a></span><span class="t"><span class="str">    However, there is a leak! Some point in the domain is constantly heated and when this has heated up its environment</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t475" href="#t475">475</a></span><span class="t"><span class="str">    sufficiently, there will be a runaway effect heating up the entire magnet.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t476" href="#t476">476</a></span><span class="t"><span class="str">    This effect has actually lead to huge magnets being destroyed at CERN in the past and hence warrants investigation.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t477" href="#t477">477</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t478" href="#t478">478</a></span><span class="t"><span class="str">    The model we use is a 1d heat equation with Neumann-zero boundary conditions, meaning this magnet is totally</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t479" href="#t479">479</a></span><span class="t"><span class="str">    insulated from its environment except for the leak.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t480" href="#t480">480</a></span><span class="t"><span class="str">    We add a non-linear term that heats parts of the domain that exceed a certain temperature threshold as well as the</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t481" href="#t481">481</a></span><span class="t"><span class="str">    leak itself.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t482" href="#t482">482</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t483" href="#t483">483</a></span><span class="t"><span class="str">    The problem is discretised with finite difference in space and treated *semi-implicitly*.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t484" href="#t484">484</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t485" href="#t485">485</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t486" href="#t486">486</a></span><span class="t">    <span class="nam">dtype_f</span> <span class="op">=</span> <span class="nam">imex_mesh</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t487" href="#t487">487</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t488" href="#t488">488</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t489" href="#t489">489</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t490" href="#t490">490</a></span><span class="t"><span class="str">        Routine to evaluate the right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t459" href="#t459">459</a></span><span class="t">                <span class="nam">uend</span><span class="op">,</span> <span class="nam">stats</span> <span class="op">=</span> <span class="nam">controller</span><span class="op">.</span><span class="nam">run</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t460" href="#t460">460</a></span><span class="t">                    <span class="nam">u0</span><span class="op">=</span><span class="nam">u_init</span> <span class="key">if</span> <span class="nam">u_init</span> <span class="key">is</span> <span class="key">not</span> <span class="key">None</span> <span class="key">else</span> <span class="nam">self</span><span class="op">.</span><span class="nam">u_exact</span><span class="op">(</span><span class="nam">t</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t461" href="#t461">461</a></span><span class="t">                    <span class="nam">t0</span><span class="op">=</span><span class="nam">t_init</span> <span class="key">if</span> <span class="nam">t_init</span> <span class="key">is</span> <span class="key">not</span> <span class="key">None</span> <span class="key">else</span> <span class="num">0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t462" href="#t462">462</a></span><span class="t">                    <span class="nam">Tend</span><span class="op">=</span><span class="nam">t</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t463" href="#t463">463</a></span><span class="t">                <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t464" href="#t464">464</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t465" href="#t465">465</a></span><span class="t">                <span class="nam">u_last</span> <span class="op">=</span> <span class="nam">get_sorted</span><span class="op">(</span><span class="nam">stats</span><span class="op">,</span> <span class="nam">type</span><span class="op">=</span><span class="str">'u'</span><span class="op">,</span> <span class="nam">recomputed</span><span class="op">=</span><span class="key">False</span><span class="op">)</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t466" href="#t466">466</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t467" href="#t467">467</a></span><span class="t">                <span class="key">if</span> <span class="nam">abs</span><span class="op">(</span><span class="nam">u_last</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">-</span> <span class="nam">t</span><span class="op">)</span> <span class="op">></span> <span class="num">1e-2</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t468" href="#t468">468</a></span><span class="t">                    <span class="nam">self</span><span class="op">.</span><span class="nam">logger</span><span class="op">.</span><span class="nam">warning</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t469" href="#t469">469</a></span><span class="t">                        <span class="str">f'Time difference between reference solution and requested time is {abs(u_last[0]-t):.2e}!'</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t470" href="#t470">470</a></span><span class="t">                    <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t471" href="#t471">471</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t472" href="#t472">472</a></span><span class="t">                <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">u_last</span><span class="op">[</span><span class="num">1</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t473" href="#t473">473</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t474" href="#t474">474</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t475" href="#t475">475</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t476" href="#t476">476</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t477" href="#t477">477</a></span><span class="t"><span class="key">class</span> <span class="nam">QuenchIMEX</span><span class="op">(</span><span class="nam">Quench</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t478" href="#t478">478</a></span><span class="t">    <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t479" href="#t479">479</a></span><span class="t"><span class="str">    This is a toy problem [1]_ to emulate a magnet that has been cooled to temperatures where superconductivity is possible.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t480" href="#t480">480</a></span><span class="t"><span class="str">    However, there is a leak! Some point in the domain is constantly heated and when this has heated up its environment</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t481" href="#t481">481</a></span><span class="t"><span class="str">    sufficiently, there will be a runaway effect heating up the entire magnet.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t482" href="#t482">482</a></span><span class="t"><span class="str">    This effect has actually lead to huge magnets being destroyed at CERN in the past and hence warrants investigation.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t483" href="#t483">483</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t484" href="#t484">484</a></span><span class="t"><span class="str">    The model we use is a 1d heat equation with Neumann-zero boundary conditions, meaning this magnet is totally</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t485" href="#t485">485</a></span><span class="t"><span class="str">    insulated from its environment except for the leak.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t486" href="#t486">486</a></span><span class="t"><span class="str">    We add a non-linear term that heats parts of the domain that exceed a certain temperature threshold as well as the</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t487" href="#t487">487</a></span><span class="t"><span class="str">    leak itself.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t488" href="#t488">488</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t489" href="#t489">489</a></span><span class="t"><span class="str">    The problem is discretised with finite difference in space and treated *semi-implicitly*.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t490" href="#t490">490</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t491" href="#t491">491</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t492" href="#t492">492</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t493" href="#t493">493</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t494" href="#t494">494</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t495" href="#t495">495</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t496" href="#t496">496</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t497" href="#t497">497</a></span><span class="t"><span class="str">            Current time of the numerical solution is computed.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t498" href="#t498">498</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t499" href="#t499">499</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t500" href="#t500">500</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t501" href="#t501">501</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t502" href="#t502">502</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t503" href="#t503">503</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t492" href="#t492">492</a></span><span class="t">    <span class="nam">dtype_f</span> <span class="op">=</span> <span class="nam">imex_mesh</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t493" href="#t493">493</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t494" href="#t494">494</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t495" href="#t495">495</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t496" href="#t496">496</a></span><span class="t"><span class="str">        Routine to evaluate the right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t497" href="#t497">497</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t498" href="#t498">498</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t499" href="#t499">499</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t500" href="#t500">500</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t501" href="#t501">501</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t502" href="#t502">502</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t503" href="#t503">503</a></span><span class="t"><span class="str">            Current time of the numerical solution is computed.</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t504" href="#t504">504</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t505" href="#t505">505</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t506" href="#t506">506</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">impl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t507" href="#t507">507</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">expl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eval_f_non_linear</span><span class="op">(</span><span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">b</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t508" href="#t508">508</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t509" href="#t509">509</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'rhs'</span><span class="op">]</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t510" href="#t510">510</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t511" href="#t511">511</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t512" href="#t512">512</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t513" href="#t513">513</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t514" href="#t514">514</a></span><span class="t"><span class="str">        Simple linear solver for :math:`(I - factor \cdot f_{expl})(\vec{u}) = \vec{rhs}`.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t515" href="#t515">515</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t516" href="#t516">516</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t517" href="#t517">517</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t518" href="#t518">518</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t519" href="#t519">519</a></span><span class="t"><span class="str">            Right-hand side for the linear system.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t520" href="#t520">520</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t521" href="#t521">521</a></span><span class="t"><span class="str">            Abbrev. for the local stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t522" href="#t522">522</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t523" href="#t523">523</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t524" href="#t524">524</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t525" href="#t525">525</a></span><span class="t"><span class="str">            Current time (e.g. for time-dependent BCs).</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t526" href="#t526">526</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t527" href="#t527">527</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t528" href="#t528">528</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t529" href="#t529">529</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t530" href="#t530">530</a></span><span class="t"><span class="str">             The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t531" href="#t531">531</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t505" href="#t505">505</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t506" href="#t506">506</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t507" href="#t507">507</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t508" href="#t508">508</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t509" href="#t509">509</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t510" href="#t510">510</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t511" href="#t511">511</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t512" href="#t512">512</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">impl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">.</span><span class="nam">dot</span><span class="op">(</span><span class="nam">u</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t513" href="#t513">513</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">expl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eval_f_non_linear</span><span class="op">(</span><span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">b</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t514" href="#t514">514</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t515" href="#t515">515</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">work_counters</span><span class="op">[</span><span class="str">'rhs'</span><span class="op">]</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t516" href="#t516">516</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t517" href="#t517">517</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t518" href="#t518">518</a></span><span class="t">    <span class="key">def</span> <span class="nam">solve_system</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">,</span> <span class="nam">factor</span><span class="op">,</span> <span class="nam">u0</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t519" href="#t519">519</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t520" href="#t520">520</a></span><span class="t"><span class="str">        Simple linear solver for :math:`(I - factor \cdot f_{expl})(\vec{u}) = \vec{rhs}`.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t521" href="#t521">521</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t522" href="#t522">522</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t523" href="#t523">523</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t524" href="#t524">524</a></span><span class="t"><span class="str">        rhs : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t525" href="#t525">525</a></span><span class="t"><span class="str">            Right-hand side for the linear system.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t526" href="#t526">526</a></span><span class="t"><span class="str">        factor : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t527" href="#t527">527</a></span><span class="t"><span class="str">            Abbrev. for the local stepsize (or any other factor required).</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t528" href="#t528">528</a></span><span class="t"><span class="str">        u0 : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t529" href="#t529">529</a></span><span class="t"><span class="str">            Initial guess for the iterative solver.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t530" href="#t530">530</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t531" href="#t531">531</a></span><span class="t"><span class="str">            Current time (e.g. for time-dependent BCs).</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t532" href="#t532">532</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t533" href="#t533">533</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t534" href="#t534">534</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">spsolve</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t535" href="#t535">535</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t536" href="#t536">536</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t537" href="#t537">537</a></span><span class="t">    <span class="key">def</span> <span class="nam">u_exact</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">=</span><span class="key">None</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">=</span><span class="key">None</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t538" href="#t538">538</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t539" href="#t539">539</a></span><span class="t"><span class="str">        Routine to compute the exact solution at time :math:`t`.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t540" href="#t540">540</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t541" href="#t541">541</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t542" href="#t542">542</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t543" href="#t543">543</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t544" href="#t544">544</a></span><span class="t"><span class="str">            Time of the exact solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t545" href="#t545">545</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t546" href="#t546">546</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t547" href="#t547">547</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t548" href="#t548">548</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t549" href="#t549">549</a></span><span class="t"><span class="str">            The exact solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t550" href="#t550">550</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t551" href="#t551">551</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t552" href="#t552">552</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t553" href="#t553">553</a></span><span class="t">        <span class="key">if</span> <span class="nam">t</span> <span class="op">==</span> <span class="num">0</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t554" href="#t554">554</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">u_exact</span><span class="op">(</span><span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t555" href="#t555">555</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t556" href="#t556">556</a></span><span class="t">        <span class="key">if</span> <span class="nam">t</span> <span class="op">></span> <span class="num">0</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t557" href="#t557">557</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t558" href="#t558">558</a></span><span class="t">            <span class="key">def</span> <span class="nam">jac</span><span class="op">(</span><span class="nam">t</span><span class="op">,</span> <span class="nam">u</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t559" href="#t559">559</a></span><span class="t">                <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t560" href="#t560">560</a></span><span class="t"><span class="str">                Get the Jacobian for the implicit BDF method to use in `scipy.solve_ivp`.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t533" href="#t533">533</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t534" href="#t534">534</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t535" href="#t535">535</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t536" href="#t536">536</a></span><span class="t"><span class="str">             The solution as mesh.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t537" href="#t537">537</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t538" href="#t538">538</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t539" href="#t539">539</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t540" href="#t540">540</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">spsolve</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">Id</span> <span class="op">-</span> <span class="nam">factor</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span><span class="op">,</span> <span class="nam">rhs</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span><span class="op">)</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">nvars</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t541" href="#t541">541</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t542" href="#t542">542</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t543" href="#t543">543</a></span><span class="t">    <span class="key">def</span> <span class="nam">u_exact</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">=</span><span class="key">None</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">=</span><span class="key">None</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t544" href="#t544">544</a></span><span class="t">        <span class="str">r"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t545" href="#t545">545</a></span><span class="t"><span class="str">        Routine to compute the exact solution at time :math:`t`.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t546" href="#t546">546</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t547" href="#t547">547</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t548" href="#t548">548</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t549" href="#t549">549</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t550" href="#t550">550</a></span><span class="t"><span class="str">            Time of the exact solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t551" href="#t551">551</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t552" href="#t552">552</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t553" href="#t553">553</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t554" href="#t554">554</a></span><span class="t"><span class="str">        me : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t555" href="#t555">555</a></span><span class="t"><span class="str">            The exact solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t556" href="#t556">556</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t557" href="#t557">557</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t558" href="#t558">558</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t559" href="#t559">559</a></span><span class="t">        <span class="key">if</span> <span class="nam">t</span> <span class="op">==</span> <span class="num">0</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t560" href="#t560">560</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">u_exact</span><span class="op">(</span><span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t561" href="#t561">561</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t562" href="#t562">562</a></span><span class="t"><span class="str">                Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t563" href="#t563">563</a></span><span class="t"><span class="str">                ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t564" href="#t564">564</a></span><span class="t"><span class="str">                t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t565" href="#t565">565</a></span><span class="t"><span class="str">                    Current time.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t566" href="#t566">566</a></span><span class="t"><span class="str">                u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t567" href="#t567">567</a></span><span class="t"><span class="str">                    Current solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t568" href="#t568">568</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t569" href="#t569">569</a></span><span class="t"><span class="str">                Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t570" href="#t570">570</a></span><span class="t"><span class="str">                -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t571" href="#t571">571</a></span><span class="t"><span class="str">                scipy.sparse.csc</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t572" href="#t572">572</a></span><span class="t"><span class="str">                    The derivative of the non-linear part of the solution w.r.t. to the solution.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t573" href="#t573">573</a></span><span class="t"><span class="str">                """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t574" href="#t574">574</a></span><span class="t">                <span class="key">return</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t575" href="#t575">575</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t576" href="#t576">576</a></span><span class="t">            <span class="key">def</span> <span class="nam">eval_rhs</span><span class="op">(</span><span class="nam">t</span><span class="op">,</span> <span class="nam">u</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t577" href="#t577">577</a></span><span class="t">                <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t578" href="#t578">578</a></span><span class="t"><span class="str">                Function to pass to `scipy.solve_ivp` to evaluate the full right-hand side.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t579" href="#t579">579</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t580" href="#t580">580</a></span><span class="t"><span class="str">                Parameters</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t581" href="#t581">581</a></span><span class="t"><span class="str">                ----------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t582" href="#t582">582</a></span><span class="t"><span class="str">                t : float</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t583" href="#t583">583</a></span><span class="t"><span class="str">                    Current time</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t584" href="#t584">584</a></span><span class="t"><span class="str">                u : numpy.1darray</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t585" href="#t585">585</a></span><span class="t"><span class="str">                    Current solution</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t586" href="#t586">586</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t587" href="#t587">587</a></span><span class="t"><span class="str">                Returns</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t588" href="#t588">588</a></span><span class="t"><span class="str">                -------</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t589" href="#t589">589</a></span><span class="t"><span class="str">                numpy.1darray</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t590" href="#t590">590</a></span><span class="t"><span class="str">                    The right-hand side.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t591" href="#t591">591</a></span><span class="t"><span class="str">                """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t592" href="#t592">592</a></span><span class="t">                <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eval_f</span><span class="op">(</span><span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t593" href="#t593">593</a></span><span class="t">                <span class="key">return</span> <span class="op">(</span><span class="nam">f</span><span class="op">.</span><span class="nam">impl</span> <span class="op">+</span> <span class="nam">f</span><span class="op">.</span><span class="nam">expl</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t594" href="#t594">594</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t595" href="#t595">595</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">generate_scipy_reference_solution</span><span class="op">(</span><span class="nam">eval_rhs</span><span class="op">,</span> <span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">,</span> <span class="nam">method</span><span class="op">=</span><span class="str">'BDF'</span><span class="op">,</span> <span class="nam">jac</span><span class="op">=</span><span class="nam">jac</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t596" href="#t596">596</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t562" href="#t562">562</a></span><span class="t">        <span class="key">if</span> <span class="nam">t</span> <span class="op">></span> <span class="num">0</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t563" href="#t563">563</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t564" href="#t564">564</a></span><span class="t">            <span class="key">def</span> <span class="nam">jac</span><span class="op">(</span><span class="nam">t</span><span class="op">,</span> <span class="nam">u</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t565" href="#t565">565</a></span><span class="t">                <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t566" href="#t566">566</a></span><span class="t"><span class="str">                Get the Jacobian for the implicit BDF method to use in `scipy.solve_ivp`.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t567" href="#t567">567</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t568" href="#t568">568</a></span><span class="t"><span class="str">                Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t569" href="#t569">569</a></span><span class="t"><span class="str">                ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t570" href="#t570">570</a></span><span class="t"><span class="str">                t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t571" href="#t571">571</a></span><span class="t"><span class="str">                    Current time.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t572" href="#t572">572</a></span><span class="t"><span class="str">                u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t573" href="#t573">573</a></span><span class="t"><span class="str">                    Current solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t574" href="#t574">574</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t575" href="#t575">575</a></span><span class="t"><span class="str">                Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t576" href="#t576">576</a></span><span class="t"><span class="str">                -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t577" href="#t577">577</a></span><span class="t"><span class="str">                scipy.sparse.csc</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t578" href="#t578">578</a></span><span class="t"><span class="str">                    The derivative of the non-linear part of the solution w.r.t. to the solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t579" href="#t579">579</a></span><span class="t"><span class="str">                """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t580" href="#t580">580</a></span><span class="t">                <span class="key">return</span> <span class="nam">self</span><span class="op">.</span><span class="nam">A</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t581" href="#t581">581</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t582" href="#t582">582</a></span><span class="t">            <span class="key">def</span> <span class="nam">eval_rhs</span><span class="op">(</span><span class="nam">t</span><span class="op">,</span> <span class="nam">u</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t583" href="#t583">583</a></span><span class="t">                <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t584" href="#t584">584</a></span><span class="t"><span class="str">                Function to pass to `scipy.solve_ivp` to evaluate the full right-hand side.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t585" href="#t585">585</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t586" href="#t586">586</a></span><span class="t"><span class="str">                Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t587" href="#t587">587</a></span><span class="t"><span class="str">                ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t588" href="#t588">588</a></span><span class="t"><span class="str">                t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t589" href="#t589">589</a></span><span class="t"><span class="str">                    Current time</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t590" href="#t590">590</a></span><span class="t"><span class="str">                u : numpy.1darray</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t591" href="#t591">591</a></span><span class="t"><span class="str">                    Current solution</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t592" href="#t592">592</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t593" href="#t593">593</a></span><span class="t"><span class="str">                Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t594" href="#t594">594</a></span><span class="t"><span class="str">                -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t595" href="#t595">595</a></span><span class="t"><span class="str">                numpy.1darray</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t596" href="#t596">596</a></span><span class="t"><span class="str">                    The right-hand side.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t597" href="#t597">597</a></span><span class="t"><span class="str">                """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t598" href="#t598">598</a></span><span class="t">                <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">eval_f</span><span class="op">(</span><span class="nam">u</span><span class="op">.</span><span class="nam">reshape</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t599" href="#t599">599</a></span><span class="t">                <span class="key">return</span> <span class="op">(</span><span class="nam">f</span><span class="op">.</span><span class="nam">impl</span> <span class="op">+</span> <span class="nam">f</span><span class="op">.</span><span class="nam">expl</span><span class="op">)</span><span class="op">.</span><span class="nam">flatten</span><span class="op">(</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t600" href="#t600">600</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t601" href="#t601">601</a></span><span class="t">            <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">generate_scipy_reference_solution</span><span class="op">(</span><span class="nam">eval_rhs</span><span class="op">,</span> <span class="nam">t</span><span class="op">,</span> <span class="nam">u_init</span><span class="op">,</span> <span class="nam">t_init</span><span class="op">,</span> <span class="nam">method</span><span class="op">=</span><span class="str">'BDF'</span><span class="op">,</span> <span class="nam">jac</span><span class="op">=</span><span class="nam">jac</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t602" href="#t602">602</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
 </main>
 <footer>
     <div class="content">
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             &nbsp; &nbsp; &nbsp;
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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+++ b/coverage/d_91faa57f8583c837_TestEquation_0D_py.html
@@ -65,7 +65,7 @@ <h2>
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+            created at 2023-11-10 06:59 +0000
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         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -236,7 +236,7 @@ <h2>
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+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_91faa57f8583c837_Van_der_Pol_implicit_py.html b/coverage/d_91faa57f8583c837_Van_der_Pol_implicit_py.html
index 20e4888c84..56b621dcdf 100644
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+++ b/coverage/d_91faa57f8583c837_Van_der_Pol_implicit_py.html
@@ -65,7 +65,7 @@ <h2>
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -265,7 +265,7 @@ <h2>
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             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_91faa57f8583c837_VorticityVelocity_2D_FEniCS_periodic_py.html b/coverage/d_91faa57f8583c837_VorticityVelocity_2D_FEniCS_periodic_py.html
index 546b853d1e..c7cabd92c5 100644
--- a/coverage/d_91faa57f8583c837_VorticityVelocity_2D_FEniCS_periodic_py.html
+++ b/coverage/d_91faa57f8583c837_VorticityVelocity_2D_FEniCS_periodic_py.html
@@ -65,7 +65,7 @@ <h2>
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             &nbsp; &nbsp; &nbsp;
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+            created at 2023-11-10 06:59 +0000
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         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -418,7 +418,7 @@ <h2>
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             &nbsp; &nbsp; &nbsp;
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_91faa57f8583c837_generic_ND_FD_py.html b/coverage/d_91faa57f8583c837_generic_ND_FD_py.html
index 4695d9d374..d9799bda0a 100644
--- a/coverage/d_91faa57f8583c837_generic_ND_FD_py.html
+++ b/coverage/d_91faa57f8583c837_generic_ND_FD_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_91faa57f8583c837_nonlinear_ODE_1_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
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+            created at 2023-11-10 06:59 +0000
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         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -351,7 +351,7 @@ <h2>
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             &nbsp; &nbsp; &nbsp;
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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 </footer>
diff --git a/coverage/d_91faa57f8583c837_nonlinear_ODE_1_py.html b/coverage/d_91faa57f8583c837_nonlinear_ODE_1_py.html
index 670060f33d..621db2be55 100644
--- a/coverage/d_91faa57f8583c837_nonlinear_ODE_1_py.html
+++ b/coverage/d_91faa57f8583c837_nonlinear_ODE_1_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_91faa57f8583c837_polynomial_test_problem_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
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+            created at 2023-11-10 06:59 +0000
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             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -239,7 +239,7 @@ <h2>
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             &nbsp; &nbsp; &nbsp;
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+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_91faa57f8583c837_polynomial_test_problem_py.html b/coverage/d_91faa57f8583c837_polynomial_test_problem_py.html
index 5497f6a37a..d0595f1169 100644
--- a/coverage/d_91faa57f8583c837_polynomial_test_problem_py.html
+++ b/coverage/d_91faa57f8583c837_polynomial_test_problem_py.html
@@ -2,7 +2,7 @@
 <html>
 <head>
     <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
-    <title>Coverage for pySDC/implementations/problem_classes/polynomial_test_problem.py: 95%</title>
+    <title>Coverage for pySDC/implementations/problem_classes/polynomial_test_problem.py: 97%</title>
     <link rel="icon" sizes="32x32" href="favicon_32.png">
     <link rel="stylesheet" href="style.css" type="text/css">
     <script type="text/javascript" src="coverage_html.js" defer></script>
@@ -12,7 +12,7 @@
     <div class="content">
         <h1>
             <span class="text">Coverage for </span><b>pySDC/implementations/problem_classes/polynomial_test_problem.py</b>:
-            <span class="pc_cov">95%</span>
+            <span class="pc_cov">97%</span>
         </h1>
         <aside id="help_panel_wrapper">
             <input id="help_panel_state" type="checkbox">
@@ -54,8 +54,8 @@ <h1>
             </div>
         </aside>
         <h2>
-            <span class="text">21 statements &nbsp;</span>
-            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">20<span class="text"> run</span></button>
+            <span class="text">29 statements &nbsp;</span>
+            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">28<span class="text"> run</span></button>
             <button type="button" class="mis show_mis button_toggle_mis" value="mis" data-shortcut="m" title="Toggle lines missing">1<span class="text"> missing</span></button>
             <button type="button" class="exc show_exc button_toggle_exc" value="exc" data-shortcut="x" title="Toggle lines excluded">1<span class="text"> excluded</span></button>
         </h2>
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_b9c274c7ffe3e178_Multistep_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -83,7 +83,7 @@ <h2>
     <p class="run"><span class="n"><a id="t1" href="#t1">1</a></span><span class="t"><span class="key">import</span> <span class="nam">numpy</span> <span class="key">as</span> <span class="nam">np</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t2" href="#t2">2</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
     <p class="run"><span class="n"><a id="t3" href="#t3">3</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">core</span><span class="op">.</span><span class="nam">Problem</span> <span class="key">import</span> <span class="nam">ptype</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t4" href="#t4">4</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">datatype_classes</span><span class="op">.</span><span class="nam">mesh</span> <span class="key">import</span> <span class="nam">mesh</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t4" href="#t4">4</a></span><span class="t"><span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">datatype_classes</span><span class="op">.</span><span class="nam">mesh</span> <span class="key">import</span> <span class="nam">mesh</span><span class="op">,</span> <span class="nam">imex_mesh</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t5" href="#t5">5</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t6" href="#t6">6</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
     <p class="run"><span class="n"><a id="t7" href="#t7">7</a></span><span class="t"><span class="key">class</span> <span class="nam">polynomial_testequation</span><span class="op">(</span><span class="nam">ptype</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
@@ -170,6 +170,38 @@ <h2>
     <p class="run"><span class="n"><a id="t88" href="#t88">88</a></span><span class="t">        <span class="nam">me</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="run"><span class="n"><a id="t89" href="#t89">89</a></span><span class="t">        <span class="nam">me</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">poly</span><span class="op">(</span><span class="nam">t</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
     <p class="run"><span class="n"><a id="t90" href="#t90">90</a></span><span class="t">        <span class="key">return</span> <span class="nam">me</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t91" href="#t91">91</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t92" href="#t92">92</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t93" href="#t93">93</a></span><span class="t"><span class="key">class</span> <span class="nam">polynomial_testequation_IMEX</span><span class="op">(</span><span class="nam">polynomial_testequation</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t94" href="#t94">94</a></span><span class="t">    <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t95" href="#t95">95</a></span><span class="t"><span class="str">    IMEX version of the polynomial test problem that assigns half the derivative to the implicit part and the other half to the explicit part.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t96" href="#t96">96</a></span><span class="t"><span class="str">    Keep in mind that you still cannot Really perform any solves.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t97" href="#t97">97</a></span><span class="t"><span class="str">    """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t98" href="#t98">98</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t99" href="#t99">99</a></span><span class="t">    <span class="nam">dtype_f</span> <span class="op">=</span> <span class="nam">imex_mesh</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t100" href="#t100">100</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t101" href="#t101">101</a></span><span class="t">    <span class="key">def</span> <span class="nam">eval_f</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">u</span><span class="op">,</span> <span class="nam">t</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t102" href="#t102">102</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t103" href="#t103">103</a></span><span class="t"><span class="str">        Derivative of the polynomial.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t104" href="#t104">104</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t105" href="#t105">105</a></span><span class="t"><span class="str">        Parameters</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t106" href="#t106">106</a></span><span class="t"><span class="str">        ----------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t107" href="#t107">107</a></span><span class="t"><span class="str">        u : dtype_u</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t108" href="#t108">108</a></span><span class="t"><span class="str">            Current values of the numerical solution.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t109" href="#t109">109</a></span><span class="t"><span class="str">        t : float</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t110" href="#t110">110</a></span><span class="t"><span class="str">            Current time of the numerical solution is computed.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t111" href="#t111">111</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t112" href="#t112">112</a></span><span class="t"><span class="str">        Returns</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t113" href="#t113">113</a></span><span class="t"><span class="str">        -------</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t114" href="#t114">114</a></span><span class="t"><span class="str">        f : dtype_f</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t115" href="#t115">115</a></span><span class="t"><span class="str">            The right-hand side of the problem.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t116" href="#t116">116</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t117" href="#t117">117</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t118" href="#t118">118</a></span><span class="t">        <span class="nam">f</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">dtype_f</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">init</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t119" href="#t119">119</a></span><span class="t">        <span class="nam">derivative</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">poly</span><span class="op">.</span><span class="nam">deriv</span><span class="op">(</span><span class="nam">m</span><span class="op">=</span><span class="num">1</span><span class="op">)</span><span class="op">(</span><span class="nam">t</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t120" href="#t120">120</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">impl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">derivative</span> <span class="op">/</span> <span class="num">2</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t121" href="#t121">121</a></span><span class="t">        <span class="nam">f</span><span class="op">.</span><span class="nam">expl</span><span class="op">[</span><span class="op">:</span><span class="op">]</span> <span class="op">=</span> <span class="nam">derivative</span> <span class="op">/</span> <span class="num">2</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t122" href="#t122">122</a></span><span class="t">        <span class="key">return</span> <span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
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+            created at 2023-11-10 06:59 +0000
         </p>
     </div>
 </footer>
diff --git a/coverage/d_c28af68f8f845bbd_estimate_extrapolation_error_py.html b/coverage/d_c28af68f8f845bbd_estimate_extrapolation_error_py.html
index 3d14a32999..f4ca6c733e 100644
--- a/coverage/d_c28af68f8f845bbd_estimate_extrapolation_error_py.html
+++ b/coverage/d_c28af68f8f845bbd_estimate_extrapolation_error_py.html
@@ -2,7 +2,7 @@
 <html>
 <head>
     <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
-    <title>Coverage for pySDC/implementations/convergence_controller_classes/estimate_extrapolation_error.py: 98%</title>
+    <title>Coverage for pySDC/implementations/convergence_controller_classes/estimate_extrapolation_error.py: 97%</title>
     <link rel="icon" sizes="32x32" href="favicon_32.png">
     <link rel="stylesheet" href="style.css" type="text/css">
     <script type="text/javascript" src="coverage_html.js" defer></script>
@@ -12,7 +12,7 @@
     <div class="content">
         <h1>
             <span class="text">Coverage for </span><b>pySDC/implementations/convergence_controller_classes/estimate_extrapolation_error.py</b>:
-            <span class="pc_cov">98%</span>
+            <span class="pc_cov">97%</span>
         </h1>
         <aside id="help_panel_wrapper">
             <input id="help_panel_state" type="checkbox">
@@ -54,9 +54,9 @@ <h1>
             </div>
         </aside>
         <h2>
-            <span class="text">164 statements &nbsp;</span>
-            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">160<span class="text"> run</span></button>
-            <button type="button" class="mis show_mis button_toggle_mis" value="mis" data-shortcut="m" title="Toggle lines missing">4<span class="text"> missing</span></button>
+            <span class="text">167 statements &nbsp;</span>
+            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">162<span class="text"> run</span></button>
+            <button type="button" class="mis show_mis button_toggle_mis" value="mis" data-shortcut="m" title="Toggle lines missing">5<span class="text"> missing</span></button>
             <button type="button" class="exc show_exc button_toggle_exc" value="exc" data-shortcut="x" title="Toggle lines excluded">8<span class="text"> excluded</span></button>
         </h2>
         <p class="text">
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_c28af68f8f845bbd_estimate_polynomial_error_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -541,72 +541,77 @@ <h2>
     <p class="run"><span class="n"><a id="t459" href="#t459">459</a></span><span class="t">        <span class="nam">default_params</span> <span class="op">=</span> <span class="op">{</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t460" href="#t460">460</a></span><span class="t">            <span class="str">'Taylor_order'</span><span class="op">:</span> <span class="num">2</span> <span class="op">*</span> <span class="nam">num_nodes</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t461" href="#t461">461</a></span><span class="t">            <span class="str">'n'</span><span class="op">:</span> <span class="nam">num_nodes</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t462" href="#t462">462</a></span><span class="t">        <span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t463" href="#t463">463</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t464" href="#t464">464</a></span><span class="t">        <span class="key">return</span> <span class="op">{</span><span class="op">**</span><span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">setup</span><span class="op">(</span><span class="nam">controller</span><span class="op">,</span> <span class="nam">params</span><span class="op">,</span> <span class="nam">description</span><span class="op">,</span> <span class="op">**</span><span class="nam">kwargs</span><span class="op">)</span><span class="op">,</span> <span class="op">**</span><span class="nam">default_params</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t462" href="#t462">462</a></span><span class="t">            <span class="str">'recompute_coefficients'</span><span class="op">:</span> <span class="key">False</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t463" href="#t463">463</a></span><span class="t">            <span class="op">**</span><span class="nam">params</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t464" href="#t464">464</a></span><span class="t">        <span class="op">}</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t465" href="#t465">465</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t466" href="#t466">466</a></span><span class="t">    <span class="key">def</span> <span class="nam">post_iteration_processing</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">controller</span><span class="op">,</span> <span class="nam">S</span><span class="op">,</span> <span class="op">**</span><span class="nam">kwargs</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t467" href="#t467">467</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t468" href="#t468">468</a></span><span class="t"><span class="str">        Compute the extrapolated error estimate here if the step is converged.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t469" href="#t469">469</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t470" href="#t470">470</a></span><span class="t"><span class="str">        Args:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t471" href="#t471">471</a></span><span class="t"><span class="str">            controller (pySDC.Controller): The controller</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t472" href="#t472">472</a></span><span class="t"><span class="str">            S (pySDC.Step): The current step</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t473" href="#t473">473</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t474" href="#t474">474</a></span><span class="t"><span class="str">        Returns:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t475" href="#t475">475</a></span><span class="t"><span class="str">            None</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t476" href="#t476">476</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t477" href="#t477">477</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t478" href="#t478">478</a></span><span class="t">        <span class="key">if</span> <span class="key">not</span> <span class="nam">self</span><span class="op">.</span><span class="nam">check_convergence</span><span class="op">(</span><span class="nam">S</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t479" href="#t479">479</a></span><span class="t">            <span class="key">return</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t480" href="#t480">480</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t481" href="#t481">481</a></span><span class="t">        <span class="nam">lvl</span> <span class="op">=</span> <span class="nam">S</span><span class="op">.</span><span class="nam">levels</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t466" href="#t466">466</a></span><span class="t">        <span class="key">return</span> <span class="op">{</span><span class="op">**</span><span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">setup</span><span class="op">(</span><span class="nam">controller</span><span class="op">,</span> <span class="nam">params</span><span class="op">,</span> <span class="nam">description</span><span class="op">,</span> <span class="op">**</span><span class="nam">kwargs</span><span class="op">)</span><span class="op">,</span> <span class="op">**</span><span class="nam">default_params</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t467" href="#t467">467</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t468" href="#t468">468</a></span><span class="t">    <span class="key">def</span> <span class="nam">post_iteration_processing</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">controller</span><span class="op">,</span> <span class="nam">S</span><span class="op">,</span> <span class="op">**</span><span class="nam">kwargs</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t469" href="#t469">469</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t470" href="#t470">470</a></span><span class="t"><span class="str">        Compute the extrapolated error estimate here if the step is converged.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t471" href="#t471">471</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t472" href="#t472">472</a></span><span class="t"><span class="str">        Args:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t473" href="#t473">473</a></span><span class="t"><span class="str">            controller (pySDC.Controller): The controller</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t474" href="#t474">474</a></span><span class="t"><span class="str">            S (pySDC.Step): The current step</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t475" href="#t475">475</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t476" href="#t476">476</a></span><span class="t"><span class="str">        Returns:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t477" href="#t477">477</a></span><span class="t"><span class="str">            None</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t478" href="#t478">478</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t479" href="#t479">479</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t480" href="#t480">480</a></span><span class="t">        <span class="key">if</span> <span class="key">not</span> <span class="nam">self</span><span class="op">.</span><span class="nam">check_convergence</span><span class="op">(</span><span class="nam">S</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t481" href="#t481">481</a></span><span class="t">            <span class="key">return</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t482" href="#t482">482</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t483" href="#t483">483</a></span><span class="t">        <span class="nam">nodes_</span> <span class="op">=</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">sweep</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">nodes</span> <span class="op">*</span> <span class="nam">S</span><span class="op">.</span><span class="nam">dt</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t484" href="#t484">484</a></span><span class="t">        <span class="nam">nodes</span> <span class="op">=</span> <span class="nam">S</span><span class="op">.</span><span class="nam">time</span> <span class="op">+</span> <span class="nam">np</span><span class="op">.</span><span class="nam">append</span><span class="op">(</span><span class="num">0</span><span class="op">,</span> <span class="nam">nodes_</span><span class="op">[</span><span class="op">:</span><span class="op">-</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t485" href="#t485">485</a></span><span class="t">        <span class="nam">t_eval</span> <span class="op">=</span> <span class="nam">S</span><span class="op">.</span><span class="nam">time</span> <span class="op">+</span> <span class="nam">nodes_</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t486" href="#t486">486</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t487" href="#t487">487</a></span><span class="t">        <span class="nam">dts</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">append</span><span class="op">(</span><span class="nam">nodes_</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">,</span> <span class="nam">nodes_</span><span class="op">[</span><span class="num">1</span><span class="op">:</span><span class="op">]</span> <span class="op">-</span> <span class="nam">nodes_</span><span class="op">[</span><span class="op">:</span><span class="op">-</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t488" href="#t488">488</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">Taylor_order</span> <span class="op">=</span> <span class="num">2</span> <span class="op">*</span> <span class="nam">len</span><span class="op">(</span><span class="nam">nodes</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t489" href="#t489">489</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">n</span> <span class="op">=</span> <span class="nam">len</span><span class="op">(</span><span class="nam">nodes</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t490" href="#t490">490</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t491" href="#t491">491</a></span><span class="t">        <span class="com"># compute the extrapolation coefficients</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t492" href="#t492">492</a></span><span class="t">        <span class="com"># TODO: Maybe this can be reused</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t493" href="#t493">493</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">get_extrapolation_coefficients</span><span class="op">(</span><span class="nam">nodes</span><span class="op">,</span> <span class="nam">dts</span><span class="op">,</span> <span class="nam">t_eval</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t494" href="#t494">494</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t495" href="#t495">495</a></span><span class="t">        <span class="com"># compute the extrapolated solution</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t496" href="#t496">496</a></span><span class="t">        <span class="key">if</span> <span class="nam">type</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span> <span class="op">==</span> <span class="nam">imex_mesh</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t497" href="#t497">497</a></span><span class="t">            <span class="nam">f</span> <span class="op">=</span> <span class="op">[</span><span class="nam">me</span><span class="op">.</span><span class="nam">impl</span> <span class="op">+</span> <span class="nam">me</span><span class="op">.</span><span class="nam">expl</span> <span class="key">for</span> <span class="nam">me</span> <span class="key">in</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t498" href="#t498">498</a></span><span class="t">        <span class="key">elif</span> <span class="nam">type</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span> <span class="op">==</span> <span class="nam">mesh</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t499" href="#t499">499</a></span><span class="t">            <span class="nam">f</span> <span class="op">=</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t500" href="#t500">500</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="exc show_exc"><span class="n"><a id="t501" href="#t501">501</a></span><span class="t">            <span class="key">raise</span> <span class="nam">DataError</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t502" href="#t502">502</a></span><span class="t">                <span class="str">f"Unable to store f from datatype {type(lvl.f[0])}, extrapolation based error estimate only\</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t503" href="#t503">503</a></span><span class="t"><span class="str"> works with types imex_mesh and mesh"</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t504" href="#t504">504</a></span><span class="t">            <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t505" href="#t505">505</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t506" href="#t506">506</a></span><span class="t">        <span class="com"># compute the error with the weighted sum</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t507" href="#t507">507</a></span><span class="t">        <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t508" href="#t508">508</a></span><span class="t">            <span class="nam">idx</span> <span class="op">=</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">rank</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span> <span class="op">%</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">size</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t509" href="#t509">509</a></span><span class="t">            <span class="nam">sendbuf</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">idx</span><span class="op">]</span> <span class="op">*</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">idx</span><span class="op">]</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">idx</span><span class="op">]</span> <span class="op">*</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">idx</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t510" href="#t510">510</a></span><span class="t">            <span class="nam">u_ex</span> <span class="op">=</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">prob</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">prob</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span> <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">rank</span> <span class="op">==</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">size</span> <span class="op">-</span> <span class="num">1</span> <span class="key">else</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t511" href="#t511">511</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">Reduce</span><span class="op">(</span><span class="nam">sendbuf</span><span class="op">,</span> <span class="nam">u_ex</span><span class="op">,</span> <span class="nam">op</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">sum</span><span class="op">,</span> <span class="nam">root</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">size</span> <span class="op">-</span> <span class="num">1</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t512" href="#t512">512</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t513" href="#t513">513</a></span><span class="t">            <span class="nam">u_ex</span> <span class="op">=</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">prob</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">prob</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t514" href="#t514">514</a></span><span class="t">            <span class="key">for</span> <span class="nam">i</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">n</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t515" href="#t515">515</a></span><span class="t">                <span class="nam">u_ex</span> <span class="op">+=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span> <span class="op">*</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span> <span class="op">*</span> <span class="nam">f</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t516" href="#t516">516</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t517" href="#t517">517</a></span><span class="t">        <span class="com"># store the error</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t518" href="#t518">518</a></span><span class="t">        <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t519" href="#t519">519</a></span><span class="t">            <span class="nam">error</span> <span class="op">=</span> <span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t520" href="#t520">520</a></span><span class="t">                <span class="nam">abs</span><span class="op">(</span><span class="nam">u_ex</span> <span class="op">-</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">rank</span> <span class="op">+</span> <span class="num">1</span><span class="op">]</span><span class="op">)</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">prefactor</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t521" href="#t521">521</a></span><span class="t">                <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">rank</span> <span class="op">==</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">size</span> <span class="op">-</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t522" href="#t522">522</a></span><span class="t">                <span class="key">else</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t523" href="#t523">523</a></span><span class="t">            <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t524" href="#t524">524</a></span><span class="t">            <span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">error_extrapolation_estimate</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">bcast</span><span class="op">(</span><span class="nam">error</span><span class="op">,</span> <span class="nam">root</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">size</span> <span class="op">-</span> <span class="num">1</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t525" href="#t525">525</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t526" href="#t526">526</a></span><span class="t">            <span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">error_extrapolation_estimate</span> <span class="op">=</span> <span class="nam">abs</span><span class="op">(</span><span class="nam">u_ex</span> <span class="op">-</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span><span class="op">)</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">prefactor</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t527" href="#t527">527</a></span><span class="t">        <span class="key">return</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t483" href="#t483">483</a></span><span class="t">        <span class="nam">lvl</span> <span class="op">=</span> <span class="nam">S</span><span class="op">.</span><span class="nam">levels</span><span class="op">[</span><span class="num">0</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t484" href="#t484">484</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t485" href="#t485">485</a></span><span class="t">        <span class="nam">nodes_</span> <span class="op">=</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">sweep</span><span class="op">.</span><span class="nam">coll</span><span class="op">.</span><span class="nam">nodes</span> <span class="op">*</span> <span class="nam">S</span><span class="op">.</span><span class="nam">dt</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t486" href="#t486">486</a></span><span class="t">        <span class="nam">nodes</span> <span class="op">=</span> <span class="nam">S</span><span class="op">.</span><span class="nam">time</span> <span class="op">+</span> <span class="nam">np</span><span class="op">.</span><span class="nam">append</span><span class="op">(</span><span class="num">0</span><span class="op">,</span> <span class="nam">nodes_</span><span class="op">[</span><span class="op">:</span><span class="op">-</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t487" href="#t487">487</a></span><span class="t">        <span class="nam">t_eval</span> <span class="op">=</span> <span class="nam">S</span><span class="op">.</span><span class="nam">time</span> <span class="op">+</span> <span class="nam">nodes_</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t488" href="#t488">488</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t489" href="#t489">489</a></span><span class="t">        <span class="nam">dts</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">append</span><span class="op">(</span><span class="nam">nodes_</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">,</span> <span class="nam">nodes_</span><span class="op">[</span><span class="num">1</span><span class="op">:</span><span class="op">]</span> <span class="op">-</span> <span class="nam">nodes_</span><span class="op">[</span><span class="op">:</span><span class="op">-</span><span class="num">1</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t490" href="#t490">490</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">Taylor_order</span> <span class="op">=</span> <span class="nam">len</span><span class="op">(</span><span class="nam">nodes</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t491" href="#t491">491</a></span><span class="t">        <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">n</span> <span class="op">=</span> <span class="nam">len</span><span class="op">(</span><span class="nam">nodes</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t492" href="#t492">492</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t493" href="#t493">493</a></span><span class="t">        <span class="com"># compute the extrapolation coefficients</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t494" href="#t494">494</a></span><span class="t">        <span class="key">if</span> <span class="key">None</span> <span class="key">in</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">u</span> <span class="key">or</span> <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">recompute_coefficients</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t495" href="#t495">495</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">get_extrapolation_coefficients</span><span class="op">(</span><span class="nam">nodes</span><span class="op">,</span> <span class="nam">dts</span><span class="op">,</span> <span class="nam">t_eval</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t496" href="#t496">496</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t497" href="#t497">497</a></span><span class="t">        <span class="com"># compute the extrapolated solution</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t498" href="#t498">498</a></span><span class="t">        <span class="key">if</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="key">is</span> <span class="key">None</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t499" href="#t499">499</a></span><span class="t">            <span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">=</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">prob</span><span class="op">.</span><span class="nam">eval_f</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">,</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">time</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t500" href="#t500">500</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t501" href="#t501">501</a></span><span class="t">        <span class="key">if</span> <span class="nam">type</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span> <span class="op">==</span> <span class="nam">imex_mesh</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t502" href="#t502">502</a></span><span class="t">            <span class="nam">f</span> <span class="op">=</span> <span class="op">[</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span><span class="op">.</span><span class="nam">impl</span> <span class="op">+</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span><span class="op">.</span><span class="nam">expl</span> <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span> <span class="key">and</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span> <span class="key">else</span> <span class="num">0.0</span> <span class="key">for</span> <span class="nam">i</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">len</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">)</span> <span class="op">-</span> <span class="num">1</span><span class="op">)</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t503" href="#t503">503</a></span><span class="t">        <span class="key">elif</span> <span class="nam">type</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="op">)</span> <span class="op">==</span> <span class="nam">mesh</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t504" href="#t504">504</a></span><span class="t">            <span class="nam">f</span> <span class="op">=</span> <span class="op">[</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span> <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span> <span class="key">else</span> <span class="num">0.0</span> <span class="key">for</span> <span class="nam">i</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">len</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">f</span><span class="op">)</span> <span class="op">-</span> <span class="num">1</span><span class="op">)</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t505" href="#t505">505</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="exc show_exc"><span class="n"><a id="t506" href="#t506">506</a></span><span class="t">            <span class="key">raise</span> <span class="nam">DataError</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t507" href="#t507">507</a></span><span class="t">                <span class="str">f"Unable to store f from datatype {type(lvl.f[0])}, extrapolation based error estimate only\</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t508" href="#t508">508</a></span><span class="t"><span class="str"> works with types imex_mesh and mesh"</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t509" href="#t509">509</a></span><span class="t">            <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t510" href="#t510">510</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t511" href="#t511">511</a></span><span class="t">        <span class="com"># compute the error with the weighted sum</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t512" href="#t512">512</a></span><span class="t">        <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t513" href="#t513">513</a></span><span class="t">            <span class="nam">idx</span> <span class="op">=</span> <span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">rank</span> <span class="op">+</span> <span class="num">1</span><span class="op">)</span> <span class="op">%</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">size</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t514" href="#t514">514</a></span><span class="t">            <span class="nam">sendbuf</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">idx</span><span class="op">]</span> <span class="op">*</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">idx</span><span class="op">]</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">idx</span><span class="op">]</span> <span class="op">*</span> <span class="nam">f</span><span class="op">[</span><span class="nam">idx</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t515" href="#t515">515</a></span><span class="t">            <span class="nam">u_ex</span> <span class="op">=</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">prob</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">prob</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span> <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">rank</span> <span class="op">==</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">size</span> <span class="op">-</span> <span class="num">1</span> <span class="key">else</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t516" href="#t516">516</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">Reduce</span><span class="op">(</span><span class="nam">sendbuf</span><span class="op">,</span> <span class="nam">u_ex</span><span class="op">,</span> <span class="nam">op</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">sum</span><span class="op">,</span> <span class="nam">root</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">size</span> <span class="op">-</span> <span class="num">1</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t517" href="#t517">517</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t518" href="#t518">518</a></span><span class="t">            <span class="nam">u_ex</span> <span class="op">=</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">prob</span><span class="op">.</span><span class="nam">dtype_u</span><span class="op">(</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">prob</span><span class="op">.</span><span class="nam">init</span><span class="op">,</span> <span class="nam">val</span><span class="op">=</span><span class="num">0.0</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t519" href="#t519">519</a></span><span class="t">            <span class="key">for</span> <span class="nam">i</span> <span class="key">in</span> <span class="nam">range</span><span class="op">(</span><span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">n</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t520" href="#t520">520</a></span><span class="t">                <span class="nam">u_ex</span> <span class="op">+=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span> <span class="op">*</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span> <span class="op">+</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">f</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span> <span class="op">*</span> <span class="nam">f</span><span class="op">[</span><span class="nam">i</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t521" href="#t521">521</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t522" href="#t522">522</a></span><span class="t">        <span class="com"># store the error</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t523" href="#t523">523</a></span><span class="t">        <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t524" href="#t524">524</a></span><span class="t">            <span class="nam">error</span> <span class="op">=</span> <span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t525" href="#t525">525</a></span><span class="t">                <span class="nam">abs</span><span class="op">(</span><span class="nam">u_ex</span> <span class="op">-</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">rank</span> <span class="op">+</span> <span class="num">1</span><span class="op">]</span><span class="op">)</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">prefactor</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t526" href="#t526">526</a></span><span class="t">                <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">rank</span> <span class="op">==</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">size</span> <span class="op">-</span> <span class="num">1</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t527" href="#t527">527</a></span><span class="t">                <span class="key">else</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t528" href="#t528">528</a></span><span class="t">            <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t529" href="#t529">529</a></span><span class="t">            <span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">error_extrapolation_estimate</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">bcast</span><span class="op">(</span><span class="nam">error</span><span class="op">,</span> <span class="nam">root</span><span class="op">=</span><span class="nam">self</span><span class="op">.</span><span class="nam">comm</span><span class="op">.</span><span class="nam">size</span> <span class="op">-</span> <span class="num">1</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t530" href="#t530">530</a></span><span class="t">        <span class="key">else</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t531" href="#t531">531</a></span><span class="t">            <span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">error_extrapolation_estimate</span> <span class="op">=</span> <span class="nam">abs</span><span class="op">(</span><span class="nam">u_ex</span> <span class="op">-</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">u</span><span class="op">[</span><span class="op">-</span><span class="num">1</span><span class="op">]</span><span class="op">)</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">coeff</span><span class="op">.</span><span class="nam">prefactor</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t532" href="#t532">532</a></span><span class="t">        <span class="key">return</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
 </main>
 <footer>
     <div class="content">
@@ -616,7 +621,7 @@ <h2>
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             &nbsp; &nbsp; &nbsp;
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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 </footer>
diff --git a/coverage/d_c28af68f8f845bbd_estimate_polynomial_error_py.html b/coverage/d_c28af68f8f845bbd_estimate_polynomial_error_py.html
index 407bb12a2f..ce26b3ae9b 100644
--- a/coverage/d_c28af68f8f845bbd_estimate_polynomial_error_py.html
+++ b/coverage/d_c28af68f8f845bbd_estimate_polynomial_error_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_c28af68f8f845bbd_hotrod_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
         </p>
         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -269,7 +269,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_c28af68f8f845bbd_hotrod_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_c28af68f8f845bbd_hotrod_py.html b/coverage/d_c28af68f8f845bbd_hotrod_py.html
index 303a7f0253..32701a4e3c 100644
--- a/coverage/d_c28af68f8f845bbd_hotrod_py.html
+++ b/coverage/d_c28af68f8f845bbd_hotrod_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_c28af68f8f845bbd_inexactness_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
             <a class="nav" href="https://coverage.readthedocs.io/en/7.3.2">coverage.py v7.3.2</a>,
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+            created at 2023-11-10 06:59 +0000
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@@ -245,7 +245,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_c28af68f8f845bbd_inexactness_py.html">&#xbb; next</a>
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+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_c28af68f8f845bbd_inexactness_py.html b/coverage/d_c28af68f8f845bbd_inexactness_py.html
index 381622a3a6..4480f3e481 100644
--- a/coverage/d_c28af68f8f845bbd_inexactness_py.html
+++ b/coverage/d_c28af68f8f845bbd_inexactness_py.html
@@ -2,7 +2,7 @@
 <html>
 <head>
     <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
-    <title>Coverage for pySDC/implementations/convergence_controller_classes/inexactness.py: 100%</title>
+    <title>Coverage for pySDC/implementations/convergence_controller_classes/inexactness.py: 83%</title>
     <link rel="icon" sizes="32x32" href="favicon_32.png">
     <link rel="stylesheet" href="style.css" type="text/css">
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@@ -12,7 +12,7 @@
     <div class="content">
         <h1>
             <span class="text">Coverage for </span><b>pySDC/implementations/convergence_controller_classes/inexactness.py</b>:
-            <span class="pc_cov">100%</span>
+            <span class="pc_cov">83%</span>
         </h1>
         <aside id="help_panel_wrapper">
             <input id="help_panel_state" type="checkbox">
@@ -54,9 +54,9 @@ <h1>
             </div>
         </aside>
         <h2>
-            <span class="text">9 statements &nbsp;</span>
-            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">9<span class="text"> run</span></button>
-            <button type="button" class="mis show_mis button_toggle_mis" value="mis" data-shortcut="m" title="Toggle lines missing">0<span class="text"> missing</span></button>
+            <span class="text">24 statements &nbsp;</span>
+            <button type="button" class="run button_toggle_run" value="run" data-shortcut="r" title="Toggle lines run">20<span class="text"> run</span></button>
+            <button type="button" class="mis show_mis button_toggle_mis" value="mis" data-shortcut="m" title="Toggle lines missing">4<span class="text"> missing</span></button>
             <button type="button" class="exc show_exc button_toggle_exc" value="exc" data-shortcut="x" title="Toggle lines excluded">1<span class="text"> excluded</span></button>
         </h2>
         <p class="text">
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_c28af68f8f845bbd_interpolate_between_restarts_py.html">&#xbb; next</a>
             &nbsp; &nbsp; &nbsp;
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+            created at 2023-11-10 06:59 +0000
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         <aside class="hidden">
             <button type="button" class="button_next_chunk" data-shortcut="j"/>
@@ -106,26 +106,67 @@ <h2>
     <p class="pln"><span class="n"><a id="t24" href="#t24">24</a></span><span class="t">            <span class="str">"ratio"</span><span class="op">:</span> <span class="num">1e-2</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t25" href="#t25">25</a></span><span class="t">            <span class="str">"min_tol"</span><span class="op">:</span> <span class="num">0</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
     <p class="pln"><span class="n"><a id="t26" href="#t26">26</a></span><span class="t">            <span class="str">"max_tol"</span><span class="op">:</span> <span class="num">1e99</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t27" href="#t27">27</a></span><span class="t">        <span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t28" href="#t28">28</a></span><span class="t">        <span class="key">return</span> <span class="op">{</span><span class="op">**</span><span class="nam">defaults</span><span class="op">,</span> <span class="op">**</span><span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">setup</span><span class="op">(</span><span class="nam">controller</span><span class="op">,</span> <span class="nam">params</span><span class="op">,</span> <span class="nam">description</span><span class="op">,</span> <span class="op">**</span><span class="nam">kwargs</span><span class="op">)</span><span class="op">}</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t29" href="#t29">29</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t30" href="#t30">30</a></span><span class="t">    <span class="key">def</span> <span class="nam">post_iteration_processing</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">controller</span><span class="op">,</span> <span class="nam">step</span><span class="op">,</span> <span class="op">**</span><span class="nam">kwargs</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t31" href="#t31">31</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t32" href="#t32">32</a></span><span class="t"><span class="str">        Change the Newton tolerance after every iteration.</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t33" href="#t33">33</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t34" href="#t34">34</a></span><span class="t"><span class="str">        Args:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t35" href="#t35">35</a></span><span class="t"><span class="str">            controller (pySDC.Controller.controller): The controller</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t36" href="#t36">36</a></span><span class="t"><span class="str">            S (pySDC.Step): The current step</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t37" href="#t37">37</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t38" href="#t38">38</a></span><span class="t"><span class="str">        Returns:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t39" href="#t39">39</a></span><span class="t"><span class="str">            None</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t40" href="#t40">40</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t41" href="#t41">41</a></span><span class="t">        <span class="key">for</span> <span class="nam">lvl</span> <span class="key">in</span> <span class="nam">step</span><span class="op">.</span><span class="nam">levels</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t42" href="#t42">42</a></span><span class="t">            <span class="nam">lvl</span><span class="op">.</span><span class="nam">prob</span><span class="op">.</span><span class="nam">newton_tol</span> <span class="op">=</span> <span class="nam">max</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t43" href="#t43">43</a></span><span class="t">                <span class="op">[</span><span class="nam">min</span><span class="op">(</span><span class="op">[</span><span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">residual</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">ratio</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">max_tol</span><span class="op">]</span><span class="op">)</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">min_tol</span><span class="op">]</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t44" href="#t44">44</a></span><span class="t">            <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
-    <p class="pln"><span class="n"><a id="t45" href="#t45">45</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
-    <p class="run"><span class="n"><a id="t46" href="#t46">46</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">log</span><span class="op">(</span><span class="str">f'Changed Newton tolerance to {lvl.prob.newton_tol:.2e}'</span><span class="op">,</span> <span class="nam">step</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t27" href="#t27">27</a></span><span class="t">            <span class="str">"maxiter"</span><span class="op">:</span> <span class="key">None</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t28" href="#t28">28</a></span><span class="t">            <span class="str">"use_e_tol"</span><span class="op">:</span> <span class="str">'e_tol'</span> <span class="key">in</span> <span class="nam">description</span><span class="op">[</span><span class="str">'level_params'</span><span class="op">]</span><span class="op">.</span><span class="nam">keys</span><span class="op">(</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t29" href="#t29">29</a></span><span class="t">            <span class="str">"initial_tol"</span><span class="op">:</span> <span class="num">1e-3</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t30" href="#t30">30</a></span><span class="t">            <span class="op">**</span><span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">setup</span><span class="op">(</span><span class="nam">controller</span><span class="op">,</span> <span class="nam">params</span><span class="op">,</span> <span class="nam">description</span><span class="op">,</span> <span class="op">**</span><span class="nam">kwargs</span><span class="op">)</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t31" href="#t31">31</a></span><span class="t">        <span class="op">}</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t32" href="#t32">32</a></span><span class="t">        <span class="key">if</span> <span class="nam">defaults</span><span class="op">[</span><span class="str">'maxiter'</span><span class="op">]</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t33" href="#t33">33</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">set_maxiter</span><span class="op">(</span><span class="nam">description</span><span class="op">,</span> <span class="nam">defaults</span><span class="op">[</span><span class="str">'maxiter'</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t34" href="#t34">34</a></span><span class="t">        <span class="key">return</span> <span class="nam">defaults</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t35" href="#t35">35</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t36" href="#t36">36</a></span><span class="t">    <span class="key">def</span> <span class="nam">dependencies</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">controller</span><span class="op">,</span> <span class="nam">description</span><span class="op">,</span> <span class="op">**</span><span class="nam">kwargs</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t37" href="#t37">37</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t38" href="#t38">38</a></span><span class="t"><span class="str">        Load the embedded error estimator if needed.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t39" href="#t39">39</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t40" href="#t40">40</a></span><span class="t"><span class="str">        Args:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t41" href="#t41">41</a></span><span class="t"><span class="str">            controller (pySDC.Controller): The controller</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t42" href="#t42">42</a></span><span class="t"><span class="str">            description (dict): The description object used to instantiate the controller</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t43" href="#t43">43</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t44" href="#t44">44</a></span><span class="t"><span class="str">        Returns:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t45" href="#t45">45</a></span><span class="t"><span class="str">            None</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t46" href="#t46">46</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t47" href="#t47">47</a></span><span class="t">        <span class="nam">super</span><span class="op">(</span><span class="op">)</span><span class="op">.</span><span class="nam">dependencies</span><span class="op">(</span><span class="nam">controller</span><span class="op">,</span> <span class="nam">description</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t48" href="#t48">48</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t49" href="#t49">49</a></span><span class="t">        <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">use_e_tol</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t50" href="#t50">50</a></span><span class="t">            <span class="key">from</span> <span class="nam">pySDC</span><span class="op">.</span><span class="nam">implementations</span><span class="op">.</span><span class="nam">convergence_controller_classes</span><span class="op">.</span><span class="nam">estimate_embedded_error</span> <span class="key">import</span> <span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t51" href="#t51">51</a></span><span class="t">                <span class="nam">EstimateEmbeddedError</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t52" href="#t52">52</a></span><span class="t">            <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t53" href="#t53">53</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t54" href="#t54">54</a></span><span class="t">            <span class="nam">controller</span><span class="op">.</span><span class="nam">add_convergence_controller</span><span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t55" href="#t55">55</a></span><span class="t">                <span class="nam">EstimateEmbeddedError</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t56" href="#t56">56</a></span><span class="t">                <span class="nam">description</span><span class="op">=</span><span class="nam">description</span><span class="op">,</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t57" href="#t57">57</a></span><span class="t">            <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t58" href="#t58">58</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t59" href="#t59">59</a></span><span class="t">        <span class="key">return</span> <span class="key">None</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t60" href="#t60">60</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t61" href="#t61">61</a></span><span class="t">    <span class="key">def</span> <span class="nam">post_iteration_processing</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">controller</span><span class="op">,</span> <span class="nam">step</span><span class="op">,</span> <span class="op">**</span><span class="nam">kwargs</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t62" href="#t62">62</a></span><span class="t">        <span class="str">"""</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t63" href="#t63">63</a></span><span class="t"><span class="str">        Change the Newton tolerance after every iteration.</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t64" href="#t64">64</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t65" href="#t65">65</a></span><span class="t"><span class="str">        Args:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t66" href="#t66">66</a></span><span class="t"><span class="str">            controller (pySDC.Controller.controller): The controller</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t67" href="#t67">67</a></span><span class="t"><span class="str">            S (pySDC.Step): The current step</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t68" href="#t68">68</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t69" href="#t69">69</a></span><span class="t"><span class="str">        Returns:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t70" href="#t70">70</a></span><span class="t"><span class="str">            None</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t71" href="#t71">71</a></span><span class="t"><span class="str">        """</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t72" href="#t72">72</a></span><span class="t">        <span class="key">for</span> <span class="nam">lvl</span> <span class="key">in</span> <span class="nam">step</span><span class="op">.</span><span class="nam">levels</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t73" href="#t73">73</a></span><span class="t">            <span class="nam">SDC_accuracy</span> <span class="op">=</span> <span class="op">(</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t74" href="#t74">74</a></span><span class="t">                <span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">get</span><span class="op">(</span><span class="str">'error_embedded_estimate'</span><span class="op">,</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">residual</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t75" href="#t75">75</a></span><span class="t">                <span class="key">if</span> <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">use_e_tol</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t76" href="#t76">76</a></span><span class="t">                <span class="key">else</span> <span class="nam">lvl</span><span class="op">.</span><span class="nam">status</span><span class="op">.</span><span class="nam">residual</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t77" href="#t77">77</a></span><span class="t">            <span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t78" href="#t78">78</a></span><span class="t">            <span class="nam">SDC_accuracy</span> <span class="op">=</span> <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">initial_tol</span> <span class="key">if</span> <span class="nam">SDC_accuracy</span> <span class="key">is</span> <span class="key">None</span> <span class="key">else</span> <span class="nam">SDC_accuracy</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t79" href="#t79">79</a></span><span class="t">            <span class="nam">tol</span> <span class="op">=</span> <span class="nam">max</span><span class="op">(</span><span class="op">[</span><span class="nam">min</span><span class="op">(</span><span class="op">[</span><span class="nam">SDC_accuracy</span> <span class="op">*</span> <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">ratio</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">max_tol</span><span class="op">]</span><span class="op">)</span><span class="op">,</span> <span class="nam">self</span><span class="op">.</span><span class="nam">params</span><span class="op">.</span><span class="nam">min_tol</span><span class="op">]</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t80" href="#t80">80</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">set_tolerance</span><span class="op">(</span><span class="nam">lvl</span><span class="op">,</span> <span class="nam">tol</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t81" href="#t81">81</a></span><span class="t">            <span class="nam">self</span><span class="op">.</span><span class="nam">log</span><span class="op">(</span><span class="str">f'Changed tolerance to {tol:.2e}'</span><span class="op">,</span> <span class="nam">step</span><span class="op">)</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t82" href="#t82">82</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t83" href="#t83">83</a></span><span class="t">    <span class="key">def</span> <span class="nam">set_tolerance</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">lvl</span><span class="op">,</span> <span class="nam">tol</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t84" href="#t84">84</a></span><span class="t">        <span class="nam">lvl</span><span class="op">.</span><span class="nam">prob</span><span class="op">.</span><span class="nam">newton_tol</span> <span class="op">=</span> <span class="nam">tol</span>&nbsp;</span><span class="r"></span></p>
+    <p class="pln"><span class="n"><a id="t85" href="#t85">85</a></span><span class="t">&nbsp;</span><span class="r"></span></p>
+    <p class="run"><span class="n"><a id="t86" href="#t86">86</a></span><span class="t">    <span class="key">def</span> <span class="nam">set_maxiter</span><span class="op">(</span><span class="nam">self</span><span class="op">,</span> <span class="nam">description</span><span class="op">,</span> <span class="nam">maxiter</span><span class="op">)</span><span class="op">:</span>&nbsp;</span><span class="r"></span></p>
+    <p class="mis show_mis"><span class="n"><a id="t87" href="#t87">87</a></span><span class="t">        <span class="nam">description</span><span class="op">[</span><span class="str">'problem_params'</span><span class="op">]</span><span class="op">[</span><span class="str">'newton_maxiter'</span><span class="op">]</span> <span class="op">=</span> <span class="nam">maxiter</span>&nbsp;</span><span class="r"></span></p>
 </main>
 <footer>
     <div class="content">
@@ -135,7 +176,7 @@ <h2>
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             &nbsp; &nbsp; &nbsp;
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-            created at 2023-11-09 08:56 +0000
+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_c28af68f8f845bbd_interpolate_between_restarts_py.html b/coverage/d_c28af68f8f845bbd_interpolate_between_restarts_py.html
index 016f5f65ce..2232bee105 100644
--- a/coverage/d_c28af68f8f845bbd_interpolate_between_restarts_py.html
+++ b/coverage/d_c28af68f8f845bbd_interpolate_between_restarts_py.html
@@ -65,7 +65,7 @@ <h2>
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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diff --git a/coverage/d_c28af68f8f845bbd_spread_step_sizes_py.html b/coverage/d_c28af68f8f845bbd_spread_step_sizes_py.html
index b0c392a517..957d0b5eb1 100644
--- a/coverage/d_c28af68f8f845bbd_spread_step_sizes_py.html
+++ b/coverage/d_c28af68f8f845bbd_spread_step_sizes_py.html
@@ -65,7 +65,7 @@ <h2>
             <a id="nextFileLink" class="nav" href="d_c28af68f8f845bbd_step_size_limiter_py.html">&#xbb; next</a>
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+            created at 2023-11-10 06:59 +0000
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@@ -316,7 +316,7 @@ <h2>
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+            created at 2023-11-10 06:59 +0000
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index 50bd930332..e073fc7934 100644
--- a/coverage/d_c28af68f8f845bbd_step_size_limiter_py.html
+++ b/coverage/d_c28af68f8f845bbd_step_size_limiter_py.html
@@ -65,7 +65,7 @@ <h2>
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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+            created at 2023-11-10 06:59 +0000
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diff --git a/genindex.html b/genindex.html
index a512d3e95a..b73bdc61c4 100644
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 </li>
@@ -835,6 +837,8 @@ <h2 id="D">D</h2>
         <li><a href="pySDC/implementations.problem_classes.Piline.html#implementations.problem_classes.Piline.piline.dtype_f">(piline attribute)</a>
 </li>
         <li><a href="pySDC/implementations.problem_classes.polynomial_test_problem.html#implementations.problem_classes.polynomial_test_problem.polynomial_testequation.dtype_f">(polynomial_testequation attribute)</a>
+</li>
+        <li><a href="pySDC/implementations.problem_classes.polynomial_test_problem.html#implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX.dtype_f">(polynomial_testequation_IMEX attribute)</a>
 </li>
         <li><a href="pySDC/core.Problem.html#core.Problem.ptype.dtype_f">(ptype attribute)</a>
 </li>
@@ -1139,6 +1143,8 @@ <h2 id="E">E</h2>
         <li><a href="pySDC/implementations.problem_classes.Piline.html#implementations.problem_classes.Piline.piline.eval_f">(piline method)</a>
 </li>
         <li><a href="pySDC/implementations.problem_classes.polynomial_test_problem.html#implementations.problem_classes.polynomial_test_problem.polynomial_testequation.eval_f">(polynomial_testequation method)</a>
+</li>
+        <li><a href="pySDC/implementations.problem_classes.polynomial_test_problem.html#implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX.eval_f">(polynomial_testequation_IMEX method)</a>
 </li>
         <li><a href="pySDC/core.Problem.html#core.Problem.ptype.eval_f">(ptype method)</a>
 </li>
@@ -3238,6 +3244,8 @@ <h2 id="P">P</h2>
       <li><a href="pySDC/core.Lagrange.html#core.Lagrange.LagrangeApproximation.points">points (LagrangeApproximation attribute)</a>
 </li>
       <li><a href="pySDC/implementations.problem_classes.polynomial_test_problem.html#implementations.problem_classes.polynomial_test_problem.polynomial_testequation">polynomial_testequation (class in implementations.problem_classes.polynomial_test_problem)</a>
+</li>
+      <li><a href="pySDC/implementations.problem_classes.polynomial_test_problem.html#implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX">polynomial_testequation_IMEX (class in implementations.problem_classes.polynomial_test_problem)</a>
 </li>
       <li><a href="pySDC/implementations.datatype_classes.particles.html#implementations.datatype_classes.particles.particles.pos">pos (particles attribute)</a>
 </li>
@@ -3623,6 +3631,10 @@ <h2 id="S">S</h2>
         <li><a href="pySDC/implementations.controller_classes.controller_nonMPI.html#implementations.controller_classes.controller_nonMPI.controller_nonMPI.send_full">(controller_nonMPI method)</a>
 </li>
       </ul></li>
+      <li><a href="pySDC/implementations.convergence_controller_classes.inexactness.html#implementations.convergence_controller_classes.inexactness.NewtonInexactness.set_maxiter">set_maxiter() (NewtonInexactness method)</a>
+</li>
+      <li><a href="pySDC/implementations.convergence_controller_classes.inexactness.html#implementations.convergence_controller_classes.inexactness.NewtonInexactness.set_tolerance">set_tolerance() (NewtonInexactness method)</a>
+</li>
       <li><a href="pySDC/implementations.convergence_controller_classes.adaptive_collocation.html#implementations.convergence_controller_classes.adaptive_collocation.AdaptiveCollocation.setup">setup() (AdaptiveCollocation method)</a>
 
       <ul>
@@ -4015,6 +4027,8 @@ <h2 id="U">U</h2>
         <li><a href="pySDC/implementations.problem_classes.AllenCahn_MPIFFT.html#implementations.problem_classes.AllenCahn_MPIFFT.allencahn_imex.u_exact">(allencahn_imex method)</a>
 </li>
         <li><a href="pySDC/implementations.problem_classes.AllenCahn_1D_FD.html#implementations.problem_classes.AllenCahn_1D_FD.allencahn_periodic_fullyimplicit.u_exact">(allencahn_periodic_fullyimplicit method)</a>
+</li>
+        <li><a href="pySDC/implementations.problem_classes.AllenCahn_2D_FD.html#implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit.u_exact">(allencahn_semiimplicit method)</a>
 </li>
         <li><a href="pySDC/implementations.problem_classes.AllenCahn_Temp_MPIFFT.html#implementations.problem_classes.AllenCahn_Temp_MPIFFT.allencahn_temp_imex.u_exact">(allencahn_temp_imex method)</a>
 </li>
diff --git a/objects.inv b/objects.inv
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diff --git a/projects/Hamiltonian.html b/projects/Hamiltonian.html
index d1d1d61cee..0ffdee2943 100644
--- a/projects/Hamiltonian.html
+++ b/projects/Hamiltonian.html
@@ -860,7 +860,7 @@ <h2>Fermi-Pasta-Ulam-Tsingou problem<a class="headerlink" href="#fermi-pasta-ula
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">7</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mi">475</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">2.10</span> <span class="o">--</span> <span class="mf">4.42</span>
-<span class="o">...</span> <span class="n">took</span> <span class="mf">56.2001</span> <span class="n">seconds</span> <span class="n">to</span> <span class="n">run</span> <span class="n">this</span><span class="o">.</span>
+<span class="o">...</span> <span class="n">took</span> <span class="mf">56.3383</span> <span class="n">seconds</span> <span class="n">to</span> <span class="n">run</span> <span class="n">this</span><span class="o">.</span>
 </pre></div>
 </div>
 <a class="reference internal image-reference" href="../_images/fput_hamiltonian.png"><img alt="../_images/fput_hamiltonian.png" src="../_images/fput_hamiltonian.png" style="width: 383.0px; height: 212.0px;" /></a>
diff --git a/projects/doc_fput.html b/projects/doc_fput.html
index e9b8d08c71..0889f45d0d 100644
--- a/projects/doc_fput.html
+++ b/projects/doc_fput.html
@@ -284,7 +284,7 @@ <h3>Navigation</h3>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">7</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mi">475</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">2.10</span> <span class="o">--</span> <span class="mf">4.42</span>
-<span class="o">...</span> <span class="n">took</span> <span class="mf">56.2001</span> <span class="n">seconds</span> <span class="n">to</span> <span class="n">run</span> <span class="n">this</span><span class="o">.</span>
+<span class="o">...</span> <span class="n">took</span> <span class="mf">56.3383</span> <span class="n">seconds</span> <span class="n">to</span> <span class="n">run</span> <span class="n">this</span><span class="o">.</span>
 </pre></div>
 </div>
 <a class="reference internal image-reference" href="../_images/fput_hamiltonian.png"><img alt="../_images/fput_hamiltonian.png" src="../_images/fput_hamiltonian.png" style="width: 383.0px; height: 212.0px;" /></a>
diff --git a/projects/doc_matrixPFASST_matrix.html b/projects/doc_matrixPFASST_matrix.html
index be28d812c8..9f980560a8 100644
--- a/projects/doc_matrixPFASST_matrix.html
+++ b/projects/doc_matrixPFASST_matrix.html
@@ -345,7 +345,7 @@ <h3>Navigation</h3>
 
 <span class="n">Working</span> <span class="k">with</span> <span class="n">diffusion</span> <span class="n">setup</span> <span class="ow">and</span> <span class="n">parameter</span> <span class="mf">1.0e+02</span><span class="o">..</span>
   <span class="n">Error</span> <span class="p">(</span><span class="n">mat</span><span class="o">/</span><span class="n">nomat</span><span class="p">)</span> <span class="n">vs</span><span class="o">.</span> <span class="n">exact</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.2887e-13</span> <span class="o">--</span> <span class="mf">3.2887e-13</span>
-  <span class="n">Difference</span> <span class="n">between</span> <span class="n">both</span> <span class="n">results</span><span class="p">:</span> <span class="mf">1.0112e-21</span>
+  <span class="n">Difference</span> <span class="n">between</span> <span class="n">both</span> <span class="n">results</span><span class="p">:</span> <span class="mf">1.0017e-21</span>
   <span class="n">Iteration</span> <span class="n">counts</span> <span class="k">for</span> <span class="n">matrix</span><span class="o">-</span><span class="n">based</span> <span class="n">version</span><span class="p">:</span> <span class="p">[(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.25</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.75</span><span class="p">,</span> <span class="mi">2</span><span class="p">)]</span>
   <span class="n">Iteration</span> <span class="n">counts</span> <span class="k">for</span> <span class="n">matrix</span><span class="o">-</span><span class="n">free</span> <span class="n">version</span><span class="p">:</span> <span class="p">[(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.25</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.75</span><span class="p">,</span> <span class="mi">2</span><span class="p">)]</span>
 
diff --git a/projects/matrixPFASST.html b/projects/matrixPFASST.html
index 076b445ffe..ec82bcec84 100644
--- a/projects/matrixPFASST.html
+++ b/projects/matrixPFASST.html
@@ -366,7 +366,7 @@ <h2>Matrix-based PFASST<a class="headerlink" href="#matrix-based-pfasst" title="
 
 <span class="n">Working</span> <span class="k">with</span> <span class="n">diffusion</span> <span class="n">setup</span> <span class="ow">and</span> <span class="n">parameter</span> <span class="mf">1.0e+02</span><span class="o">..</span>
   <span class="n">Error</span> <span class="p">(</span><span class="n">mat</span><span class="o">/</span><span class="n">nomat</span><span class="p">)</span> <span class="n">vs</span><span class="o">.</span> <span class="n">exact</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.2887e-13</span> <span class="o">--</span> <span class="mf">3.2887e-13</span>
-  <span class="n">Difference</span> <span class="n">between</span> <span class="n">both</span> <span class="n">results</span><span class="p">:</span> <span class="mf">1.0112e-21</span>
+  <span class="n">Difference</span> <span class="n">between</span> <span class="n">both</span> <span class="n">results</span><span class="p">:</span> <span class="mf">1.0017e-21</span>
   <span class="n">Iteration</span> <span class="n">counts</span> <span class="k">for</span> <span class="n">matrix</span><span class="o">-</span><span class="n">based</span> <span class="n">version</span><span class="p">:</span> <span class="p">[(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.25</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.75</span><span class="p">,</span> <span class="mi">2</span><span class="p">)]</span>
   <span class="n">Iteration</span> <span class="n">counts</span> <span class="k">for</span> <span class="n">matrix</span><span class="o">-</span><span class="n">free</span> <span class="n">version</span><span class="p">:</span> <span class="p">[(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.25</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.75</span><span class="p">,</span> <span class="mi">2</span><span class="p">)]</span>
 
diff --git a/pySDC/implementations.convergence_controller_classes.inexactness.html b/pySDC/implementations.convergence_controller_classes.inexactness.html
index 574d3f0547..c94737b471 100644
--- a/pySDC/implementations.convergence_controller_classes.inexactness.html
+++ b/pySDC/implementations.convergence_controller_classes.inexactness.html
@@ -54,6 +54,23 @@ <h3>Navigation</h3>
 <dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">ConvergenceController</span></code></p>
 <p>Gradually refine Newton tolerance based on SDC residual.
 Be aware that the problem needs a parameter called “newton_tol” which controls the tolerance for the Newton solver for this to work!</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="implementations.convergence_controller_classes.inexactness.NewtonInexactness.dependencies">
+<span class="sig-name descname"><span class="pre">dependencies</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">controller</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">description</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/convergence_controller_classes/inexactness.html#NewtonInexactness.dependencies"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.convergence_controller_classes.inexactness.NewtonInexactness.dependencies" title="Link to this definition">¶</a></dt>
+<dd><p>Load the embedded error estimator if needed.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>controller</strong> (<em>pySDC.Controller</em>) – The controller</p></li>
+<li><p><strong>description</strong> (<em>dict</em>) – The description object used to instantiate the controller</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p>None</p>
+</dd>
+</dl>
+</dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="implementations.convergence_controller_classes.inexactness.NewtonInexactness.post_iteration_processing">
 <span class="sig-name descname"><span class="pre">post_iteration_processing</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">controller</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">step</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/convergence_controller_classes/inexactness.html#NewtonInexactness.post_iteration_processing"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.convergence_controller_classes.inexactness.NewtonInexactness.post_iteration_processing" title="Link to this definition">¶</a></dt>
@@ -71,6 +88,16 @@ <h3>Navigation</h3>
 </dl>
 </dd></dl>
 
+<dl class="py method">
+<dt class="sig sig-object py" id="implementations.convergence_controller_classes.inexactness.NewtonInexactness.set_maxiter">
+<span class="sig-name descname"><span class="pre">set_maxiter</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">description</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">maxiter</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/convergence_controller_classes/inexactness.html#NewtonInexactness.set_maxiter"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.convergence_controller_classes.inexactness.NewtonInexactness.set_maxiter" title="Link to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="implementations.convergence_controller_classes.inexactness.NewtonInexactness.set_tolerance">
+<span class="sig-name descname"><span class="pre">set_tolerance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">lvl</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/convergence_controller_classes/inexactness.html#NewtonInexactness.set_tolerance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.convergence_controller_classes.inexactness.NewtonInexactness.set_tolerance" title="Link to this definition">¶</a></dt>
+<dd></dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="implementations.convergence_controller_classes.inexactness.NewtonInexactness.setup">
 <span class="sig-name descname"><span class="pre">setup</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">controller</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">params</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">description</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/convergence_controller_classes/inexactness.html#NewtonInexactness.setup"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.convergence_controller_classes.inexactness.NewtonInexactness.setup" title="Link to this definition">¶</a></dt>
@@ -108,7 +135,10 @@ <h3><a href="../index.html">Table of Contents</a></h3>
     <ul>
 <li><a class="reference internal" href="#">implementations.convergence_controller_classes.inexactness module</a><ul>
 <li><a class="reference internal" href="#implementations.convergence_controller_classes.inexactness.NewtonInexactness"><code class="docutils literal notranslate"><span class="pre">NewtonInexactness</span></code></a><ul>
+<li><a class="reference internal" href="#implementations.convergence_controller_classes.inexactness.NewtonInexactness.dependencies"><code class="docutils literal notranslate"><span class="pre">dependencies()</span></code></a></li>
 <li><a class="reference internal" href="#implementations.convergence_controller_classes.inexactness.NewtonInexactness.post_iteration_processing"><code class="docutils literal notranslate"><span class="pre">post_iteration_processing()</span></code></a></li>
+<li><a class="reference internal" href="#implementations.convergence_controller_classes.inexactness.NewtonInexactness.set_maxiter"><code class="docutils literal notranslate"><span class="pre">set_maxiter()</span></code></a></li>
+<li><a class="reference internal" href="#implementations.convergence_controller_classes.inexactness.NewtonInexactness.set_tolerance"><code class="docutils literal notranslate"><span class="pre">set_tolerance()</span></code></a></li>
 <li><a class="reference internal" href="#implementations.convergence_controller_classes.inexactness.NewtonInexactness.setup"><code class="docutils literal notranslate"><span class="pre">setup()</span></code></a></li>
 </ul>
 </li>
diff --git a/pySDC/implementations.problem_classes.AllenCahn_2D_FD.html b/pySDC/implementations.problem_classes.AllenCahn_2D_FD.html
index e9ca1e66cd..b39b95e2cf 100644
--- a/pySDC/implementations.problem_classes.AllenCahn_2D_FD.html
+++ b/pySDC/implementations.problem_classes.AllenCahn_2D_FD.html
@@ -51,7 +51,7 @@ <h3>Navigation</h3>
 <span id="implementations-problem-classes-allencahn-2d-fd-module"></span><h1>implementations.problem_classes.AllenCahn_2D_FD module<a class="headerlink" href="#module-implementations.problem_classes.AllenCahn_2D_FD" title="Link to this heading">¶</a></h1>
 <dl class="py class">
 <dt class="sig sig-object py" id="implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">allencahn_fullyimplicit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(128,</span> <span class="pre">128)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.04</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.25</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/AllenCahn_2D_FD.html#allencahn_fullyimplicit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit" title="Link to this definition">¶</a></dt>
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">allencahn_fullyimplicit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(128,</span> <span class="pre">128)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.04</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">inexact_linear_ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.25</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/AllenCahn_2D_FD.html#allencahn_fullyimplicit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit" title="Link to this definition">¶</a></dt>
 <dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">ptype</span></code></p>
 <p>Example implementing the two-dimensional Allen-Cahn equation with periodic boundary conditions <span class="math notranslate nohighlight">\(u \in [-1, 1]^2\)</span></p>
 <div class="math notranslate nohighlight">
@@ -204,7 +204,7 @@ <h3>Navigation</h3>
 
 <dl class="py method">
 <dt class="sig sig-object py" id="implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit.u_exact">
-<span class="sig-name descname"><span class="pre">u_exact</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">t</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/AllenCahn_2D_FD.html#allencahn_fullyimplicit.u_exact"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit.u_exact" title="Link to this definition">¶</a></dt>
+<span class="sig-name descname"><span class="pre">u_exact</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">t</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u_init</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">t_init</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/AllenCahn_2D_FD.html#allencahn_fullyimplicit.u_exact"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit.u_exact" title="Link to this definition">¶</a></dt>
 <dd><p>Routine to compute the exact solution at time <span class="math notranslate nohighlight">\(t\)</span>.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -223,7 +223,7 @@ <h3>Navigation</h3>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="implementations.problem_classes.AllenCahn_2D_FD.allencahn_multiimplicit">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">allencahn_multiimplicit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(128,</span> <span class="pre">128)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.04</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.25</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/AllenCahn_2D_FD.html#allencahn_multiimplicit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_multiimplicit" title="Link to this definition">¶</a></dt>
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">allencahn_multiimplicit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(128,</span> <span class="pre">128)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.04</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">inexact_linear_ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.25</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/AllenCahn_2D_FD.html#allencahn_multiimplicit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_multiimplicit" title="Link to this definition">¶</a></dt>
 <dd><p>Bases: <a class="reference internal" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit" title="implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit"><code class="xref py py-class docutils literal notranslate"><span class="pre">allencahn_fullyimplicit</span></code></a></p>
 <p>Example implementing the two-dimensional Allen-Cahn equation with periodic boundary conditions <span class="math notranslate nohighlight">\(u \in [-1, 1]^2\)</span></p>
 <div class="math notranslate nohighlight">
@@ -308,7 +308,7 @@ <h3>Navigation</h3>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="implementations.problem_classes.AllenCahn_2D_FD.allencahn_multiimplicit_v2">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">allencahn_multiimplicit_v2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(128,</span> <span class="pre">128)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.04</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.25</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/AllenCahn_2D_FD.html#allencahn_multiimplicit_v2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_multiimplicit_v2" title="Link to this definition">¶</a></dt>
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">allencahn_multiimplicit_v2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(128,</span> <span class="pre">128)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.04</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">inexact_linear_ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.25</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/AllenCahn_2D_FD.html#allencahn_multiimplicit_v2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_multiimplicit_v2" title="Link to this definition">¶</a></dt>
 <dd><p>Bases: <a class="reference internal" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit" title="implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit"><code class="xref py py-class docutils literal notranslate"><span class="pre">allencahn_fullyimplicit</span></code></a></p>
 <p>This class implements the two-dimensional Allen-Cahn (AC) equation with periodic boundary conditions <span class="math notranslate nohighlight">\(u \in [-1, 1]^2\)</span></p>
 <div class="math notranslate nohighlight">
@@ -394,7 +394,7 @@ <h3>Navigation</h3>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">allencahn_semiimplicit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(128,</span> <span class="pre">128)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.04</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.25</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/AllenCahn_2D_FD.html#allencahn_semiimplicit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit" title="Link to this definition">¶</a></dt>
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">allencahn_semiimplicit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(128,</span> <span class="pre">128)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.04</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">inexact_linear_ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.25</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/AllenCahn_2D_FD.html#allencahn_semiimplicit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit" title="Link to this definition">¶</a></dt>
 <dd><p>Bases: <a class="reference internal" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit" title="implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit"><code class="xref py py-class docutils literal notranslate"><span class="pre">allencahn_fullyimplicit</span></code></a></p>
 <p>This class implements the two-dimensional Allen-Cahn equation with periodic boundary conditions <span class="math notranslate nohighlight">\(u \in [-1, 1]^2\)</span></p>
 <div class="math notranslate nohighlight">
@@ -453,11 +453,28 @@ <h3>Navigation</h3>
 </dl>
 </dd></dl>
 
+<dl class="py method">
+<dt class="sig sig-object py" id="implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit.u_exact">
+<span class="sig-name descname"><span class="pre">u_exact</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">t</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u_init</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">t_init</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/AllenCahn_2D_FD.html#allencahn_semiimplicit.u_exact"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit.u_exact" title="Link to this definition">¶</a></dt>
+<dd><p>Routine to compute the exact solution at time t.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>t</strong> (<em>float</em>) – Time of the exact solution.</p>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>me</strong> – The exact solution.</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p>dtype_u</p>
+</dd>
+</dl>
+</dd></dl>
+
 </dd></dl>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit_v2">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">allencahn_semiimplicit_v2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(128,</span> <span class="pre">128)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.04</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.25</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/AllenCahn_2D_FD.html#allencahn_semiimplicit_v2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit_v2" title="Link to this definition">¶</a></dt>
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">allencahn_semiimplicit_v2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(128,</span> <span class="pre">128)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.04</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lin_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">inexact_linear_ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.25</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/AllenCahn_2D_FD.html#allencahn_semiimplicit_v2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit_v2" title="Link to this definition">¶</a></dt>
 <dd><p>Bases: <a class="reference internal" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit" title="implementations.problem_classes.AllenCahn_2D_FD.allencahn_fullyimplicit"><code class="xref py py-class docutils literal notranslate"><span class="pre">allencahn_fullyimplicit</span></code></a></p>
 <p>This class implements the two-dimensional Allen-Cahn (AC) equation with periodic boundary conditions <span class="math notranslate nohighlight">\(u \in [-1, 1]^2\)</span></p>
 <div class="math notranslate nohighlight">
@@ -565,6 +582,7 @@ <h3><a href="../index.html">Table of Contents</a></h3>
 <li><a class="reference internal" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit.dtype_f"><code class="docutils literal notranslate"><span class="pre">dtype_f</span></code></a></li>
 <li><a class="reference internal" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit.eval_f"><code class="docutils literal notranslate"><span class="pre">eval_f()</span></code></a></li>
 <li><a class="reference internal" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit.solve_system"><code class="docutils literal notranslate"><span class="pre">solve_system()</span></code></a></li>
+<li><a class="reference internal" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit.u_exact"><code class="docutils literal notranslate"><span class="pre">u_exact()</span></code></a></li>
 </ul>
 </li>
 <li><a class="reference internal" href="#implementations.problem_classes.AllenCahn_2D_FD.allencahn_semiimplicit_v2"><code class="docutils literal notranslate"><span class="pre">allencahn_semiimplicit_v2</span></code></a><ul>
diff --git a/pySDC/implementations.problem_classes.Quench.html b/pySDC/implementations.problem_classes.Quench.html
index 31a286ca77..a41280600c 100644
--- a/pySDC/implementations.problem_classes.Quench.html
+++ b/pySDC/implementations.problem_classes.Quench.html
@@ -51,7 +51,7 @@ <h3>Navigation</h3>
 <span id="implementations-problem-classes-quench-module"></span><h1>implementations.problem_classes.Quench module<a class="headerlink" href="#module-implementations.problem_classes.Quench" title="Link to this heading">¶</a></h1>
 <dl class="py class">
 <dt class="sig sig-object py" id="implementations.problem_classes.Quench.Quench">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Quench</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Cv</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">K</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u_thresh</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.03</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.06</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Q_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">leak_range</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(0.45,</span> <span class="pre">0.55)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">leak_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'linear'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">leak_transition</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'step'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stencil_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'center'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bc</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'neumann-zero'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">128</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">99</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lintol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">liniter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">99</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">direct_solver</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">inexact_linear_ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">reference_sol_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'scipy'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/Quench.html#Quench"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.Quench.Quench" title="Link to this definition">¶</a></dt>
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Quench</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Cv</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">K</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u_thresh</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.03</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.06</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Q_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">leak_range</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(0.45,</span> <span class="pre">0.55)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">leak_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'linear'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">leak_transition</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'step'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stencil_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'center'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bc</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'neumann-zero'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">128</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">99</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lintol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">liniter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">99</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">direct_solver</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">inexact_linear_ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_lintol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">reference_sol_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'scipy'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/Quench.html#Quench"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.Quench.Quench" title="Link to this definition">¶</a></dt>
 <dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">ptype</span></code></p>
 <p>This is a toy problem <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> to emulate a magnet that has been cooled to temperatures where superconductivity is possible.
 However, there is a leak! Some point in the domain is constantly heated and when this has heated up its environment
@@ -82,6 +82,8 @@ <h3>Navigation</h3>
 <li><p><strong>lintol</strong> (<em>float</em><em>, </em><em>optional</em>) – Tolerance for linear solver to be done.</p></li>
 <li><p><strong>liniter</strong> (<em>int</em><em>, </em><em>optional</em>) – Maximum number of linear iterations inside the Newton solver.</p></li>
 <li><p><strong>direct_solver</strong> (<em>bool</em><em>, </em><em>optional</em>) – Indicates if a direct solver should be used.</p></li>
+<li><p><strong>inexact_linear_ratio</strong> (<em>float</em><em>, </em><em>optional</em>) – Ratio of tolerance of linear solver to the Newton residual, overrides <cite>lintol</cite></p></li>
+<li><p><strong>min_lintol</strong> (<em>float</em><em>, </em><em>optional</em>) – Minimal tolerance for the linear solver</p></li>
 <li><p><strong>reference_sol_type</strong> (<em>str</em><em>, </em><em>optional</em>) – Indicates which method should be used to compute a reference solution.
 Choose between <code class="docutils literal notranslate"><span class="pre">'scipy'</span></code>, <code class="docutils literal notranslate"><span class="pre">'SDC'</span></code>, or <code class="docutils literal notranslate"><span class="pre">'DIRK'</span></code>.</p></li>
 </ul>
@@ -263,7 +265,7 @@ <h3>Navigation</h3>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="implementations.problem_classes.Quench.QuenchIMEX">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">QuenchIMEX</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Cv</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">K</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u_thresh</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.03</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.06</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Q_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">leak_range</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(0.45,</span> <span class="pre">0.55)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">leak_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'linear'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">leak_transition</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'step'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stencil_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'center'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bc</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'neumann-zero'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">128</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">99</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lintol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">liniter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">99</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">direct_solver</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">inexact_linear_ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">reference_sol_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'scipy'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/Quench.html#QuenchIMEX"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.Quench.QuenchIMEX" title="Link to this definition">¶</a></dt>
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">QuenchIMEX</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Cv</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">K</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u_thresh</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.03</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.06</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Q_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">leak_range</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(0.45,</span> <span class="pre">0.55)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">leak_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'linear'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">leak_transition</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'step'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stencil_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'center'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bc</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'neumann-zero'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nvars</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">128</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">newton_maxiter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">99</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lintol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">liniter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">99</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">direct_solver</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">inexact_linear_ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_lintol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">reference_sol_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'scipy'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/Quench.html#QuenchIMEX"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.Quench.QuenchIMEX" title="Link to this definition">¶</a></dt>
 <dd><p>Bases: <a class="reference internal" href="#implementations.problem_classes.Quench.Quench" title="implementations.problem_classes.Quench.Quench"><code class="xref py py-class docutils literal notranslate"><span class="pre">Quench</span></code></a></p>
 <p>This is a toy problem <a class="footnote-reference brackets" href="#id2" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> to emulate a magnet that has been cooled to temperatures where superconductivity is possible.
 However, there is a leak! Some point in the domain is constantly heated and when this has heated up its environment
diff --git a/pySDC/implementations.problem_classes.html b/pySDC/implementations.problem_classes.html
index b0e1f05f7e..4476f8b3f5 100644
--- a/pySDC/implementations.problem_classes.html
+++ b/pySDC/implementations.problem_classes.html
@@ -263,6 +263,7 @@ <h2>Submodules<a class="headerlink" href="#submodules" title="Link to this headi
 </li>
 <li class="toctree-l1"><a class="reference internal" href="implementations.problem_classes.polynomial_test_problem.html">implementations.problem_classes.polynomial_test_problem module</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="implementations.problem_classes.polynomial_test_problem.html#implementations.problem_classes.polynomial_test_problem.polynomial_testequation"><code class="docutils literal notranslate"><span class="pre">polynomial_testequation</span></code></a></li>
+<li class="toctree-l2"><a class="reference internal" href="implementations.problem_classes.polynomial_test_problem.html#implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX"><code class="docutils literal notranslate"><span class="pre">polynomial_testequation_IMEX</span></code></a></li>
 </ul>
 </li>
 </ul>
diff --git a/pySDC/implementations.problem_classes.polynomial_test_problem.html b/pySDC/implementations.problem_classes.polynomial_test_problem.html
index 11cd4c3b7c..2c56c6f8f8 100644
--- a/pySDC/implementations.problem_classes.polynomial_test_problem.html
+++ b/pySDC/implementations.problem_classes.polynomial_test_problem.html
@@ -131,6 +131,40 @@ <h3>Navigation</h3>
 
 </dd></dl>
 
+<dl class="py class">
+<dt class="sig sig-object py" id="implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">polynomial_testequation_IMEX</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">degree</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">seed</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">26266</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/polynomial_test_problem.html#polynomial_testequation_IMEX"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX" title="Link to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#implementations.problem_classes.polynomial_test_problem.polynomial_testequation" title="implementations.problem_classes.polynomial_test_problem.polynomial_testequation"><code class="xref py py-class docutils literal notranslate"><span class="pre">polynomial_testequation</span></code></a></p>
+<p>IMEX version of the polynomial test problem that assigns half the derivative to the implicit part and the other half to the explicit part.
+Keep in mind that you still cannot Really perform any solves.</p>
+<dl class="py attribute">
+<dt class="sig sig-object py" id="implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX.dtype_f">
+<span class="sig-name descname"><span class="pre">dtype_f</span></span><a class="headerlink" href="#implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX.dtype_f" title="Link to this definition">¶</a></dt>
+<dd><p>alias of <code class="xref py py-class docutils literal notranslate"><span class="pre">imex_mesh</span></code></p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX.eval_f">
+<span class="sig-name descname"><span class="pre">eval_f</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">u</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">t</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/implementations/problem_classes/polynomial_test_problem.html#polynomial_testequation_IMEX.eval_f"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX.eval_f" title="Link to this definition">¶</a></dt>
+<dd><p>Derivative of the polynomial.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>u</strong> (<em>dtype_u</em>) – Current values of the numerical solution.</p></li>
+<li><p><strong>t</strong> (<em>float</em>) – Current time of the numerical solution is computed.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>f</strong> – The right-hand side of the problem.</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p>dtype_f</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
 </section>
 
 
@@ -152,6 +186,11 @@ <h3><a href="../index.html">Table of Contents</a></h3>
 <li><a class="reference internal" href="#implementations.problem_classes.polynomial_test_problem.polynomial_testequation.u_exact"><code class="docutils literal notranslate"><span class="pre">u_exact()</span></code></a></li>
 </ul>
 </li>
+<li><a class="reference internal" href="#implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX"><code class="docutils literal notranslate"><span class="pre">polynomial_testequation_IMEX</span></code></a><ul>
+<li><a class="reference internal" href="#implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX.dtype_f"><code class="docutils literal notranslate"><span class="pre">dtype_f</span></code></a></li>
+<li><a class="reference internal" href="#implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX.eval_f"><code class="docutils literal notranslate"><span class="pre">eval_f()</span></code></a></li>
+</ul>
+</li>
 </ul>
 </li>
 </ul>
diff --git a/searchindex.js b/searchindex.js
index 5e75995bb7..b7165a4118 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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"&lt;no title&gt;", "&lt;no title&gt;", "&lt;no title&gt;", "&lt;no title&gt;", "Step-1: A first spatial problem", "Step-2: Data structures and my first sweeper", "Step-3: Statistics and a new sweeper", "Step-4: Multilevel SDC", "Step-5: PFASST", "Step-6: Advanced PFASST controllers", "Step-7: pySDC with external libraries", "Step-8: Advanced topics"], "terms": {"back": [0, 1, 2, 4, 5, 6, 7, 8, 165, 191], "main": [0, 1, 2, 5, 9, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 36, 39, 62, 63, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "page": [0, 1, 2, 9, 18, 53, 107, 109, 114, 120, 145], "juli": 0, "28": [0, 119], "2023": [0, 107, 109, 114, 139, 171, 173, 192, 193], "For": [0, 1, 3, 4, 6, 8, 9, 12, 15, 18, 26, 33, 34, 36, 42, 45, 62, 63, 65, 66, 88, 91, 92, 94, 95, 96, 97, 99, 102, 106, 107, 109, 120, 122, 139, 140, 144, 145, 146, 149, 150, 180, 186, 187, 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35, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "merg": [0, 4, 41], "thank": 0, "brownbaerchen": 0, "tlunet": 0, "lisawim": 0, "ikrom96git": 0, "all": [0, 1, 3, 5, 6, 9, 10, 12, 14, 16, 17, 18, 19, 26, 27, 29, 30, 33, 34, 35, 40, 41, 42, 44, 45, 46, 51, 62, 63, 65, 66, 67, 69, 70, 73, 74, 78, 85, 90, 99, 105, 115, 122, 139, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 166, 168, 172, 179, 182, 184, 185, 191, 192, 193, 194, 195, 196, 197, 198], "contribut": [0, 1, 5, 6, 7, 8], "besid": 0, "usual": [0, 6, 18, 77, 195, 197], "bugfix": 0, "polish": 0, "pysdc": [0, 4, 7, 8, 10, 11, 12, 14, 16, 19, 21, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 44, 46, 48, 49, 50, 51, 56, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 94, 99, 119, 123, 125, 126, 141, 144, 156, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 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149, 150, 152, 153, 154, 156, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198], "more": [0, 2, 3, 5, 7, 8, 9, 10, 12, 13, 16, 18, 19, 25, 32, 33, 35, 55, 66, 71, 72, 122, 169, 173, 174, 176, 177, 178, 185, 191, 192, 193, 194, 195, 197, 198], "improv": [0, 4, 6, 8, 13, 18, 193, 194], "project": [0, 3, 4, 5, 10, 12, 13, 14, 15, 16, 18, 19, 21, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 99, 108, 112, 113, 127, 157, 198], "we": [0, 1, 3, 5, 8, 9, 12, 13, 14, 15, 16, 17, 18, 25, 33, 34, 35, 36, 41, 42, 45, 53, 62, 65, 66, 67, 69, 70, 71, 72, 73, 74, 77, 78, 79, 99, 119, 124, 143, 144, 145, 169, 170, 171, 175, 176, 184, 185, 191, 192, 193, 194, 195, 196, 197, 198], "have": [0, 1, 4, 5, 6, 9, 12, 13, 15, 25, 27, 34, 35, 36, 42, 48, 65, 66, 67, 72, 73, 74, 77, 82, 83, 84, 86, 90, 92, 143, 144, 145, 169, 179, 185, 191, 192, 193, 194, 195, 196, 197, 198], "second": [0, 5, 9, 15, 21, 25, 32, 33, 34, 38, 47, 66, 73, 74, 82, 84, 91, 92, 104, 105, 106, 108, 110, 111, 114, 117, 119, 121, 144, 145, 146, 149, 150, 153, 154, 156, 190, 193, 198], "order": [0, 3, 5, 8, 9, 10, 11, 13, 15, 16, 18, 19, 21, 25, 26, 27, 29, 30, 32, 33, 34, 35, 36, 41, 42, 45, 47, 54, 58, 65, 66, 67, 69, 71, 72, 73, 74, 75, 80, 82, 84, 85, 88, 90, 91, 92, 100, 104, 106, 108, 111, 112, 113, 114, 115, 117, 122, 124, 127, 129, 130, 131, 133, 134, 135, 137, 139, 143, 144, 145, 146, 150, 152, 153, 154, 166, 168, 171, 173, 175, 181, 185, 190, 191, 192, 193, 194, 195, 197, 198], "sdc": [0, 2, 3, 9, 12, 13, 14, 18, 19, 28, 34, 50, 62, 63, 66, 68, 72, 73, 76, 78, 104, 124, 146, 150, 170, 171, 172, 173, 174, 177, 178, 181, 185, 186, 189, 190, 191, 192, 193, 195, 196, 197], "board": [0, 94, 95], "brand": 0, "new": [0, 3, 4, 5, 7, 8, 9, 11, 13, 34, 35, 50, 63, 65, 71, 77, 78, 79, 100, 107, 109, 143, 144, 145, 166, 168, 172, 184, 191, 196], "switch": [0, 65, 66, 72, 99, 101, 102], "estim": [0, 13, 15, 62, 66, 68, 71, 72, 74, 75, 99, 102, 182, 190, 196], "test": [0, 2, 3, 4, 10, 11, 12, 13, 16, 17, 18, 19, 26, 27, 33, 34, 35, 36, 68, 79, 102, 108, 112, 113, 125, 127, 141, 145, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "ground": 0, "compress": [0, 9], "libpressio": [0, 18], "march": [0, 11, 73], "24": [0, 12, 32, 144, 180, 181, 195], "2": [0, 5, 6, 7, 9, 11, 12, 14, 16, 17, 19, 21, 26, 27, 28, 29, 30, 32, 33, 34, 35, 39, 44, 48, 58, 65, 66, 73, 82, 83, 84, 86, 88, 89, 90, 91, 92, 94, 95, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 119, 120, 121, 122, 123, 124, 126, 127, 139, 140, 144, 165, 166, 168, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 193, 194, 195, 196, 197, 198], "i": [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 21, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 41, 42, 44, 45, 47, 50, 55, 62, 63, 65, 66, 67, 68, 70, 72, 73, 74, 75, 77, 78, 79, 80, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 156, 164, 165, 166, 168, 169, 170, 171, 172, 173, 175, 176, 177, 179, 180, 181, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "out": [0, 3, 9, 11, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 62, 63, 72, 122, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "code": [0, 2, 3, 4, 6, 7, 9, 10, 12, 16, 18, 19, 21, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 70, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "multipl": [0, 13, 18, 41, 42, 44, 50, 65, 73, 74, 149, 176, 181, 185, 186, 192, 193, 194, 195, 196, 197], "direct": [0, 18, 66, 79, 90, 92, 96, 97, 100, 107, 109, 114, 115, 118, 124, 139, 164, 171, 192], "The": [0, 1, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 26, 27, 33, 34, 35, 36, 38, 39, 41, 42, 45, 47, 48, 51, 53, 54, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141, 143, 144, 146, 147, 148, 149, 150, 152, 153, 154, 156, 191, 192, 194, 195, 197, 198], "problem": [0, 2, 3, 6, 9, 11, 15, 16, 17, 18, 19, 21, 25, 26, 27, 28, 29, 30, 32, 33, 34, 37, 41, 43, 46, 49, 56, 65, 66, 70, 72, 73, 74, 76, 78, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 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159, 160, 161, 162, 181, 187, 190, 195, 197, 198], "channel": [1, 5], "term": [1, 10, 47, 73, 92, 94, 95, 104, 112, 113, 114, 115, 122, 124, 192], "lead": [1, 42, 124, 144, 145, 194, 198], "seriou": [1, 198], "sustain": 1, "pattern": 1, "aggress": [1, 14, 185, 197], "disparag": 1, "www": [1, 3, 9, 12, 21, 104, 105, 110, 140], "code_of_conduct": 1, "html": [1, 5, 105, 110, 120], "inspir": [1, 6, 8, 45, 47], "mozilla": 1, "ladder": 1, "answer": [1, 18], "common": [1, 11, 13, 37], "question": [1, 18, 198], "faq": 1, "translat": 1, "develop": [2, 3, 5, 6, 8, 9, 13, 95, 119], "approach": [2, 3, 5, 9, 34, 35, 139, 185, 195, 197], "fork": [2, 4, 5], "extend": [2, 122, 193], "skip": 2, "furthermor": 2, "branch": [2, 5, 15], "pre": [2, 4, 5, 29, 30, 35, 178, 192, 194], "To": [2, 3, 5, 9, 11, 139, 193, 194, 195, 196, 197], "pleas": [2, 3, 5, 9, 15, 44, 57, 66, 72, 79, 144, 145, 149, 192, 193], "addition": [2, 91], "rule": [2, 5, 6, 45, 47, 65, 66, 72, 143, 144, 145, 154, 193], "enforc": [2, 5, 6, 42, 79], "summar": 2, "convent": [2, 5, 7], "chosen": [2, 194], "name": [2, 3, 4, 5, 7, 9, 12, 16, 19, 25, 32, 40, 42, 43, 46, 53, 55, 122, 184, 191, 192, 193, 195, 196], "function": [2, 4, 5, 7, 8, 11, 12, 13, 16, 19, 21, 25, 28, 29, 30, 32, 35, 41, 42, 44, 45, 46, 48, 50, 56, 57, 58, 62, 63, 66, 67, 69, 72, 73, 75, 77, 83, 89, 94, 95, 96, 97, 99, 101, 102, 107, 108, 109, 110, 111, 112, 113, 120, 122, 127, 141, 146, 149, 150, 164, 165, 170, 171, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "flavor": [2, 3, 9, 67, 72, 78, 178, 194, 196], "applic": [2, 4, 9, 13, 44, 57, 65, 70, 101, 191, 198], "object": [2, 6, 8, 18, 35, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 55, 56, 59, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 96, 97, 100, 107, 109, 110, 114, 120, 131, 136, 137, 143, 144, 156, 173, 174, 178, 192, 193, 194, 198], "program": [2, 5, 26, 27, 34, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "oop": 2, "custom": [2, 6, 8, 14, 38, 44, 46, 48, 49, 50, 51, 146, 147, 150, 152, 153, 154, 156, 159, 193], "inherit": [2, 7, 40, 89, 99, 149], "framework": [2, 197], "addit": [2, 4, 6, 36, 41, 56, 90, 193, 196], "guidelin": [2, 3, 5, 6, 9], "given": [2, 5, 7, 8, 36, 39, 45, 47, 49, 50, 65, 88, 89, 91, 98, 99, 103, 118, 119, 122, 126, 140, 165, 191, 195, 196, 198], "esp": [3, 9], "multilevel": [3, 9, 50], "extens": [3, 9], "intend": [3, 9, 13], "rapid": [3, 9], "purpos": [3, 9, 41, 184, 188, 192, 194, 196, 198], "predictor": [3, 9, 44, 51, 62, 63, 144, 149, 194], "toi": [3, 9, 124], "easili": [3, 6, 9, 12, 18], "variant": [3, 9, 12, 14, 19, 185, 197], "implicit": [3, 9, 11, 16, 19, 26, 29, 30, 33, 34, 35, 82, 83, 84, 86, 89, 91, 92, 99, 107, 109, 110, 112, 113, 127, 143, 144, 148, 149, 150, 152, 153, 180, 181, 186, 187, 190, 192, 195, 197, 198], "imex": [3, 9, 26, 33, 34, 88, 144, 150, 152, 170, 171, 172, 173, 174, 178, 180, 186, 187, 190, 192, 193, 194, 195, 197, 198], "verlet": [3, 9, 12, 21, 25, 32, 142, 145, 146], "diagon": [3, 9, 26, 27, 34, 35, 125, 144], "topic": [3, 9, 18], "outcom": [3, 9, 18], "gitlab": [3, 9], "10": [3, 8, 9, 12, 14, 16, 19, 21, 25, 28, 29, 30, 32, 35, 75, 97, 98, 100, 101, 105, 107, 109, 114, 119, 124, 144, 145, 166, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 185, 186, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "host": [3, 4, 9], "com": [3, 9, 45, 145], "often": [3, 9, 18, 66], "choic": [3, 5, 9, 144, 145, 195], "thu": [3, 9, 11, 13, 191, 194], "checkout": [3, 9], "conda": [3, 5, 9, 10], "found": [3, 9, 12, 13, 14, 29, 30, 33, 35, 42, 58, 99, 102, 193, 197], "folder": [3, 5, 9, 10, 197], "etc": [3, 5, 9, 36, 42, 66, 69, 73, 75, 194, 195], "env": [3, 9, 184, 196], "creat": [3, 9, 10, 12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 44, 99, 108, 112, 113, 127, 139, 165, 166, 167, 168, 169, 176, 187, 188, 191, 192, 193, 194, 195, 197, 198], "yml": [3, 9], "m": [3, 5, 8, 9, 11, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 42, 45, 63, 67, 73, 74, 75, 78, 100, 108, 112, 113, 122, 124, 127, 131, 167, 168, 171, 172, 173, 174, 177, 178, 179, 180, 181, 182, 185, 186, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "correspond": [3, 5, 9, 12, 18, 25, 26, 27, 33, 34, 42, 47, 50, 57, 65, 146, 147, 148, 149, 150, 151, 152, 153, 154, 194, 196, 198], "chose": [3, 9, 119], "pythonpath": [3, 9, 184, 196], "export": [3, 5, 9], "path": [3, 5, 9, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 42, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "root": [3, 5, 9, 11, 13, 82, 84, 86, 102, 184, 196], "want": [3, 5, 9, 18, 42, 65, 66, 67, 70, 72, 73, 78, 145, 192, 196, 198], "import": [3, 5, 6, 7, 8, 9, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 42, 73, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "statement": [3, 5, 9], "assum": [3, 9, 122, 195], "directori": [3, 5, 9, 12, 16, 19, 21, 25, 28, 32, 35, 184, 196], "decent": [3, 9], "compil": [3, 9], "although": [3, 6, 9, 10, 191, 192, 194], "go": [3, 5, 9, 14, 44, 62, 63, 77, 79, 170, 184, 192, 195, 196], "great": [3, 9], "let": [3, 8, 9, 45, 77, 91, 99, 103], "know": [3, 9, 46, 66, 73, 74, 77, 173, 192, 193, 195], "help": [3, 6, 8, 9, 36, 185, 193, 197], "greatli": [3, 9, 18], "appreci": [3, 9], "citat": [3, 9, 144], "robert": [3, 9, 18, 122], "speck": [3, 9, 88, 103, 122, 150], "997": [3, 9, 166, 191], "transact": [3, 9], "mathemat": [3, 9], "softwar": [3, 9, 108, 112, 113, 127], "volum": [3, 9], "45": [3, 9, 124, 186, 197], "doi": [3, 8, 9, 75, 98, 100, 119, 124, 144], "1145": [3, 9, 144], "3310410": [3, 9], 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21, 25, 28, 32, 35, 73, 122, 180, 181, 185, 186, 187, 190, 194, 195, 197, 198], "joint": [3, 9], "undertak": [3, 9], "ju": [3, 9], "grant": [3, 9], "agreement": [3, 9], "955701": [3, 9], "union": [3, 9], "horizon": [3, 9], "2020": [3, 9], "research": [3, 9], "innov": [3, 9], "programm": [3, 9], "belgium": [3, 9], "franc": [3, 9], "germani": [3, 9], "switzerland": [3, 9], "german": [3, 9], "feder": [3, 9], "ministri": [3, 9], "bmbf": [3, 9], "16hpc047": [3, 9], "helmholtz": [3, 9], "engin": [3, 9], "preparatori": [3, 9], "studi": [3, 9, 33, 35, 66, 104], "hirse_p": [3, 9], "nbsp": [3, 9], "done": [4, 5, 9, 10, 12, 13, 14, 16, 19, 21, 25, 28, 29, 30, 32, 35, 42, 66, 102, 106, 109, 110, 114, 124, 170, 171, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "repositori": [4, 5], "eventu": [4, 6, 9], "mainten": 4, "howev": [4, 5, 6, 18, 42, 73, 90, 124, 144, 145, 194, 198], "highli": [4, 194], "trough": 4, "dedic": [4, 101], "master": [4, 5, 9, 11, 15], "contributor": 4, "propos": 4, "solv": [4, 7, 9, 16, 18, 19, 48, 65, 66, 73, 74, 78, 89, 90, 91, 92, 94, 95, 96, 97, 99, 106, 107, 108, 109, 110, 112, 113, 115, 118, 119, 120, 122, 127, 141, 144, 145, 167, 168, 191, 197], "accuraci": [4, 10, 13, 18, 54, 65, 72, 73, 139, 165, 166, 168, 169, 190, 192, 196, 198], "issue214": 4, "214": 4, "awesome_new_project": 4, "some_featur": 4, "favor": [4, 6], "short": [4, 6, 196], "lower": [4, 5, 18, 35, 66, 72, 74, 79, 144, 145, 148, 193], "case": [4, 5, 6, 11, 13, 35, 69, 99, 102, 106, 107, 191, 194, 195, 196, 198], "underscor": [4, 6], "eas": [4, 6, 50], "interfac": [4, 18, 41, 48, 49, 51, 144, 145, 192], "modifi": [4, 5, 11, 35, 36, 47, 72], "default": [4, 5, 16, 19, 42, 44, 45, 48, 51, 55, 56, 62, 63, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 80, 108, 112, 113, 124, 127, 139, 143, 149, 192, 194], "valu": [4, 6, 7, 8, 10, 11, 12, 13, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 38, 39, 40, 41, 42, 44, 45, 46, 48, 50, 51, 54, 55, 56, 57, 58, 62, 63, 65, 66, 69, 71, 72, 73, 75, 77, 79, 82, 83, 84, 85, 86, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 122, 123, 124, 125, 126, 127, 129, 130, 133, 134, 135, 139, 140, 141, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 156, 159, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "revis": 4, "happen": [4, 26, 27, 34, 41, 42, 65, 66, 72, 77, 198], "upstream": 4, "repo": 4, "hesit": 4, "regularli": [4, 5, 13], "conflict": 4, "On": 4, "my_featur": 4, "git": [4, 5], "fetch": 4, "synchron": [4, 11], "v": [4, 5, 12, 16, 19, 21, 25, 26, 27, 30, 32, 34, 35, 91, 99, 101, 104, 108, 109, 110, 112, 113, 122, 123, 127, 165, 166, 170, 174, 177, 182, 183, 184, 187, 189, 191, 192, 193, 196, 197, 198], "next": [4, 5, 6, 7, 8, 11, 14, 18, 46, 50, 58, 65, 66, 72, 78, 99, 193, 194, 195, 196, 198], "v5": 4, "v6": 4, "forc": [4, 10, 12, 91, 96, 97, 104, 112, 113, 114, 115, 173, 178, 193, 194, 197], "re": [4, 170, 192, 194], "write": [4, 5, 12, 21, 26, 27, 28, 29, 30, 32, 34, 35, 42, 77, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "script": [4, 9, 10, 11, 16, 36, 119, 196], "anyon": 4, "onc": [4, 5, 26, 27, 34, 42, 65, 73, 74, 184, 196], "roadmap": 4, "mileston": 4, "associ": [4, 8, 45, 46, 139], "down": [4, 13, 15, 62, 63, 101], "Such": 4, "same": [4, 6, 7, 15, 18, 27, 34, 41, 42, 65, 73, 78, 89, 90, 92, 99, 115, 124, 139, 172, 179, 191, 192, 193, 194, 195, 196], "never": [4, 65, 74], "modif": [4, 54], "own": [4, 5, 18, 193], "prefix": [4, 6], "dev": 4, "cannot": [4, 7, 11, 42, 66, 194], "sever": [4, 12, 35, 90, 115], "solut": [4, 6, 7, 10, 11, 13, 15, 16, 18, 19, 26, 27, 28, 33, 34, 35, 46, 48, 65, 66, 69, 70, 72, 73, 74, 77, 80, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 122, 123, 124, 125, 126, 127, 139, 140, 141, 143, 144, 145, 165, 166, 167, 168, 170, 171, 173, 175, 177, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 191, 192, 193, 194, 195, 196, 197, 198], "summari": [4, 5, 6, 7, 8], "panel": 5, "divid": [5, 88, 100, 103, 108, 112, 113, 127, 196], "categori": 5, "build": [5, 27, 34, 54, 167, 168, 184, 191, 196], "artifact": 5, "section": 5, "style": [5, 8, 12, 16, 19, 21, 25, 28, 32, 35, 62, 63, 73], "syntax": [5, 6], "complianc": 5, "pep": [5, 6], "comprehens": [5, 65], "bugbear": 5, "diff": [5, 26, 34, 177, 189, 194, 198], "color": [5, 18, 28, 29, 30, 35, 166, 168, 187, 191, 197], "reformat": 5, "command": 5, "line": [5, 6, 11, 18, 65, 123, 139, 166, 167, 168, 184, 191, 196], "120": 5, "charact": [5, 6], "arithmet": 5, "variabl": [5, 7, 12, 25, 41, 42, 48, 50, 55, 65, 66, 67, 69, 71, 72, 73, 74, 77, 80, 100, 144, 145, 184, 193, 195, 196], "empti": [5, 184, 196], "autom": [5, 108, 112, 113, 127], "possibli": [5, 10, 65, 74, 77], "bin": 5, "sh": 5, "stage": [5, 42, 51, 62, 63, 73, 143, 144, 145, 149, 152, 171, 173, 192, 193, 198], "head": 5, "grep": [5, 29, 30, 35], "py": [5, 10, 11, 12, 14, 16, 17, 19, 21, 23, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 99, 146, 147, 150, 152, 153, 154, 158, 159, 160, 161, 162, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "sed": 5, "rev": 5, "pars": 5, "toplevel": 5, "delet": [5, 73], "becaus": [5, 18, 73, 77, 119, 149, 185, 197], "fail": [5, 184, 196], "fi": 5, "chmod": 5, "execut": [5, 196], "Be": [5, 66, 76, 79, 144], "awar": [5, 66, 76, 79, 144, 145], "alter": 5, "editor": 5, "whenev": [5, 41, 65, 191], "r": [5, 8, 16, 19, 28, 29, 30, 35, 38, 58, 88, 91, 92, 94, 95, 96, 97, 99, 100, 101, 103, 105, 106, 107, 109, 114, 121, 122, 123, 124, 139, 156, 198], "messag": [5, 42, 62, 65, 66, 69, 73, 74, 75], "detect": [5, 18, 75], "abort": [5, 26, 27, 34, 70], "ahead": 5, "worri": [5, 196], "obtain": [5, 8, 34, 35, 45, 54, 65, 66, 72, 73, 108], "msg": [5, 42, 70], "commit_msg_fil": 5, "flakeheaven_output": 5, "interpret": 5, "trailer": 5, "echo": 5, "assign": [5, 29, 30, 35], "note": [5, 6, 8, 12, 14, 16, 17, 19, 26, 27, 33, 34, 45, 72, 171, 185, 186, 191, 192, 193, 194, 195, 196, 197, 198], "relat": [5, 33, 38, 42, 48, 49, 50, 51, 156, 193], "constantli": [5, 124], "pep8": [5, 9], "might": [5, 18, 55, 77, 79, 196], "caus": [5, 15, 144, 196], "date": 5, "forg": 5, "pass": [5, 6, 8, 16, 19, 26, 27, 29, 30, 34, 35, 38, 42, 46, 48, 50, 51, 53, 57, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 78, 79, 80, 156, 179, 180, 181, 186, 187, 190, 191, 192, 194, 195, 197, 198], "toml": [5, 184, 196], "compon": [5, 10, 11, 13, 82, 83, 84, 86, 98, 110, 118, 119, 126, 140, 153, 198], "test_nod": 5, "how": [5, 8, 12, 13, 17, 18, 67, 71, 72, 73, 101, 124, 172, 191, 192, 193, 194, 195, 196, 197, 198], "compar": [5, 10, 13, 16, 19, 26, 27, 28, 33, 34, 35, 65, 66, 73, 74, 75, 94, 95, 165, 166, 170, 171, 173, 174, 175, 177, 178, 180, 181, 182, 184, 185, 187, 188, 189, 191, 192, 193, 194, 195, 196, 197, 198], "indic": [5, 6, 9, 39, 43, 58, 62, 91, 94, 95, 96, 97, 99, 101, 102, 106, 108, 112, 113, 118, 124, 126, 127, 140, 192], "print": [5, 6, 7, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "load": [5, 12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 42, 66, 67, 68, 71, 72, 75, 79, 99, 123], "sitecustom": 5, "process_startup": 5, "durat": 5, "analyz": [5, 33, 34, 36, 191], "henc": [5, 15, 18, 42, 66, 74, 112, 113, 124, 127], "finish": [5, 171, 173, 192, 193], "process": [5, 10, 15, 18, 26, 34, 36, 43, 44, 62, 73, 82, 84, 86, 108, 109, 110, 171, 173, 179, 180, 181, 182, 183, 184, 188, 189, 192, 193, 195, 196, 198], "combin": [5, 11, 12, 73, 184, 187, 194, 196, 197], "htmlcov": 5, "favorit": [5, 144], "browser": 5, "did": [5, 12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 73, 166, 167, 168, 169, 170, 171, 175, 184, 187, 191, 192, 194, 196, 197], "ignor": [5, 144, 145, 198], "rais": [5, 6, 7, 12, 16, 19, 25, 26, 27, 32, 34, 42, 70, 184, 185, 196, 197], "tool": [5, 36, 192], "pyproject": [5, 184, 196], "conditionali": 5, "loop": [5, 13, 16, 19, 28, 29, 30, 35, 44, 166, 168, 174, 180, 181, 182, 191, 193, 195, 196], "pragma": 5, "cover": 5, "def": [5, 6, 7, 8, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "preced": 5, "think": 5, "justifi": 5, "built": [5, 6, 144, 145, 192, 198], "task": [5, 196], "doc": [5, 120], "unzip": 5, "rst": 5, "update_apidoc": 5, "b": [5, 16, 19, 26, 27, 28, 29, 30, 34, 35, 65, 73, 74, 100, 108, 109, 110, 112, 113, 122, 127, 131, 137, 173, 178, 179, 180, 181, 187, 190], "Then": [5, 8, 13, 14, 45, 191, 193], "graph": [5, 28, 35], "imag": 5, "still": [5, 35, 42, 65, 74, 144], "miss": [5, 198], "concern": 5, "mostli": [6, 43], "Of": [6, 194], "cours": [6, 42, 194], "strictli": [6, 144, 145], "alwai": [6, 15, 44, 66, 78, 101, 144, 145, 146, 154, 191, 194, 196], "guido": 6, "von": 6, "rossum": 6, "kei": [6, 12, 16, 19, 21, 25, 29, 30, 32, 35, 55, 57, 62, 63, 73, 99, 139, 174, 184, 192, 193, 195, 196], "insight": 6, "state": [6, 13, 35, 96, 97, 99, 101, 102], "foolish": 6, "hobgoblin": 6, "littl": [6, 186, 191, 193, 197], "mind": [6, 48, 54, 74], "find": [6, 9, 13, 15, 18, 29, 30, 35, 42, 58, 166, 168, 191], "optim": [6, 11, 35, 66, 120, 166, 168, 191], "compromis": 6, "someon": [6, 9], "els": [6, 12, 16, 19, 25, 26, 27, 29, 30, 32, 34, 35, 66, 99, 102, 149, 178, 182, 184, 185, 186, 187, 190, 194, 196, 197, 198], "understand": [6, 8, 36], "my": [6, 9], "effect": [6, 66, 119, 124], "kilomet": 6, "aspect": [6, 18], "interdepend": 6, "attract": 6, "lowercas": 6, "variablenamelikethi": 6, "snake_cas": 6, "variable_name_like_thi": 6, "pascalcas": 6, "camelcas": 6, "uppercas": 6, "minu": 6, "try": [6, 14, 15, 65, 66, 72, 184, 191, 196], "stick": 6, "discourag": 6, "advectiondiffus": 6, "except": [6, 15, 42, 43, 47, 124, 184, 196], "suffix": [6, 195], "parametererror": [6, 37, 43], "goe": [6, 42], "argument": [6, 42, 44, 48, 57, 90, 172, 193], "tleft": [6, 39, 167, 168, 191], "quadtyp": 6, "legendr": [6, 39, 45, 47, 167, 168, 177, 191, 193, 194], "computefejerrul": [6, 37, 45], "nnode": [6, 176, 194], "nodegener": 6, "getorthogpolycoeff": 6, "self": [6, 7, 8, 42, 63, 68, 73, 99, 149], "ncoeff": 6, "abbrevi": 6, "deterior": [6, 13], "rather": [6, 8, 12, 13, 18, 33, 185, 192, 196, 197], "getorthogonalpolynomialcoeffici": 6, "plural": 6, "acronym": 6, "jacobimssdc": 6, "multistepsdcjacobi": 6, "mssdcjacobi": 6, "put": [6, 166, 191, 193, 198], "exception": 6, "special": [6, 9, 11, 12, 25, 32, 34, 92, 106, 107, 173, 174, 178, 193, 194, 198], "mysweep": 6, "initsweep": 6, "getattr": 6, "_initsweep_": 6, "attributeerror": 6, "notimplementederror": [6, 12, 16, 19, 25, 32, 185, 197], "_initsweep_copi": 6, "_initsweep_spread": 6, "_": [6, 8, 11, 12, 21, 25, 32, 45, 110, 112, 113, 120, 171, 173, 190, 192, 193, 198], "chucknorri": 6, "_think": 6, "doubt": 6, "doubl": [6, 66], "__": [6, 171, 173, 192, 193], "left": [6, 11, 12, 14, 21, 25, 32, 33, 39, 45, 54, 58, 90, 91, 92, 94, 95, 96, 97, 106, 107, 112, 114, 115, 117, 122, 139, 150, 166, 168, 191], "__dict__": [6, 55], "node_typ": [6, 39, 47, 167, 168, 177, 191, 194], "equid": [6, 39], "chebi": [6, 39], "quad_typ": [6, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 39, 47, 167, 168, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "gauss": [6, 15, 18, 35, 39, 45, 47, 66, 72, 174, 193, 195, 198], "radau": [6, 16, 19, 26, 27, 28, 29, 30, 34, 35, 39, 167, 168, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "lobatto": [6, 12, 21, 25, 32, 39, 47, 174, 193], "string": [6, 16, 19, 41, 42, 46, 57, 139], "distinguish": 6, "select": [6, 66, 74], "probabl": [6, 122, 197], "keep": [6, 10, 41, 42, 48, 54, 74, 182, 196], "replac": [6, 14, 16, 19, 193, 194], "_initsweep_copy_past": 6, "_initsweep_spread_out": 6, "non": [7, 17, 35, 42, 58, 62, 66, 67, 69, 73, 78, 82, 84, 85, 86, 119, 124, 196], "od": [7, 9, 48, 51, 98, 99, 101, 119, 123, 140, 143, 149, 194, 197], "form": [7, 9, 11, 90, 92, 94, 95, 96, 97, 108, 109, 110, 113, 115, 118, 125, 146, 150, 185, 191, 195, 197], "frac": [7, 8, 45, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 139, 140], "du": [7, 16, 19, 108, 109, 110, 118, 140], "dt": [7, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 45, 46, 50, 66, 73, 98, 99, 101, 102, 103, 111, 117, 118, 119, 122, 123, 125, 126, 131, 137, 139, 140, 167, 168, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "quad": 7, "u_0": [7, 11, 103], "vector": [7, 8, 11, 45, 54, 58, 65, 73, 74, 104, 105, 107, 108, 109, 112, 113, 121, 127, 158, 162, 167, 168, 191, 192], "scalar": [7, 8, 33, 45, 103, 108, 112, 113, 127, 146, 150], "hand": [7, 18, 42, 48, 51, 54, 65, 73, 77, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 154, 167, 168, 191, 192, 194, 197], "side": [7, 18, 48, 51, 54, 65, 77, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 154, 167, 168, 191, 192, 194, 197], "ptype": [7, 37, 46, 48, 49, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 113, 114, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141], "templat": [7, 36], "lambda": [7, 12, 16, 19, 21, 25, 26, 27, 32, 34, 103, 118, 122, 125, 146, 150, 184, 196], "ct": 7, "complex": [7, 9, 12, 33, 84, 193], "np": [7, 8, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 45, 47, 58, 65, 74, 83, 88, 89, 91, 92, 94, 96, 97, 99, 100, 101, 103, 104, 122, 123, 124, 139, 165, 166, 167, 168, 173, 174, 175, 178, 180, 181, 184, 185, 186, 187, 190, 191, 193, 194, 195, 196, 197, 198], "problemerror": [7, 37, 43], "datatype_class": [7, 10, 60, 166, 171, 173, 191, 192, 193, 197], "mycustomproblem": 7, "datatyp": [7, 10, 42, 82, 84, 161], "dtype_u": [7, 46, 48, 50, 72, 73, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141, 143, 144, 146, 147, 148, 149, 150, 151, 153, 154, 165, 166, 175, 191, 194], "dtype_f": [7, 46, 48, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141, 143, 144, 145], "lam": [7, 118], "len": [7, 12, 16, 19, 21, 27, 29, 30, 32, 34, 35, 166, 168, 175, 176, 179, 184, 187, 191, 194, 195, 196, 197], "shape": [7, 38], "must": [7, 8, 45, 48, 99, 194], "1d": [7, 16, 17, 33, 54, 58, 88, 91, 106, 124, 159, 191], "call": [7, 12, 13, 16, 19, 21, 25, 28, 29, 30, 32, 35, 41, 42, 44, 48, 50, 57, 66, 67, 72, 76, 77, 80, 91, 92, 99, 101, 109, 110, 114, 122, 126, 140, 149, 171, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "super": [7, 42, 44, 110, 193], "init": [7, 8, 42, 48, 82, 83, 84, 85, 86, 165, 166, 175, 181, 191, 194, 195], "none": [7, 10, 12, 16, 19, 25, 26, 27, 28, 29, 30, 32, 34, 35, 39, 41, 42, 44, 46, 48, 54, 55, 57, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 82, 83, 84, 85, 86, 88, 94, 95, 96, 97, 99, 100, 102, 104, 107, 108, 109, 110, 114, 119, 120, 123, 124, 125, 126, 127, 139, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 166, 168, 171, 173, 182, 185, 186, 190, 191, 192, 193, 196, 197, 198], "dtype": [7, 84, 173, 174, 178, 193, 194], "regist": [7, 40, 57, 172, 193], "localvar": 7, "true": [7, 12, 16, 19, 26, 27, 32, 34, 42, 46, 53, 58, 73, 91, 99, 102, 106, 110, 118, 119, 120, 124, 126, 139, 140, 144, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "rh": [7, 10, 38, 46, 48, 51, 73, 82, 83, 84, 86, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 106, 107, 108, 109, 110, 112, 113, 114, 118, 119, 120, 122, 123, 124, 125, 126, 127, 131, 137, 139, 140, 141, 143, 149, 156], "eval_f": [7, 48, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141, 165, 166, 191], "f_init": [7, 48], "list": [7, 8, 9, 10, 12, 16, 19, 21, 25, 26, 27, 29, 30, 32, 34, 35, 41, 42, 45, 46, 48, 50, 53, 54, 57, 58, 63, 65, 67, 73, 74, 75, 78, 91, 94, 95, 96, 97, 99, 100, 102, 104, 108, 125, 127, 143, 144, 146, 147, 148, 149, 150, 151, 153, 154, 166, 168, 172, 173, 174, 175, 178, 180, 181, 182, 184, 189, 191, 193, 194, 195, 196, 198], "output": [7, 12, 13, 25, 32, 36, 44, 48, 65, 107, 109, 159, 173, 174, 178, 182, 184, 187, 193, 194, 196, 197], "fals": [7, 12, 16, 19, 32, 41, 42, 44, 53, 54, 58, 62, 63, 67, 72, 105, 118, 120, 121, 139, 147, 148, 149, 150, 151, 152, 153, 171, 173, 178, 182, 185, 186, 187, 189, 190, 192, 193, 194, 196, 197, 198], "docstr": 8, "itself": [8, 13, 42, 73, 124, 194, 198], "describ": [8, 9, 11, 16, 17, 19, 36, 99, 105, 108, 109, 110, 121, 172, 193], "lagrangeapproxim": [8, 37, 45], "approxim": [8, 11, 18, 45, 73, 74, 89, 91, 94, 95, 96, 97, 110, 118, 119, 120, 123, 124, 126], "point": [8, 13, 18, 39, 45, 46, 47, 53, 58, 65, 72, 73, 74, 89, 91, 92, 94, 95, 96, 97, 99, 102, 105, 107, 121, 124, 146, 147, 148, 149, 150, 151, 152, 153, 154, 165, 166, 191], "lagrang": [8, 37, 108, 112, 113, 127, 194], "math": [8, 100, 107], "t_j": [8, 45], "leq": [8, 45, 99, 101, 102, 115, 140], "j": [8, 45, 88, 92, 94, 95, 96, 97, 101, 103, 104, 105, 107, 108, 109, 112, 113, 121, 127, 144], "n": [8, 12, 16, 19, 21, 26, 27, 28, 32, 34, 35, 45, 90, 92, 94, 95, 96, 97, 99, 100, 104, 105, 106, 108, 110, 112, 113, 115, 120, 121, 122, 127, 129, 130, 133, 134, 135, 137, 139, 166, 167, 168, 170, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "formula": [8, 45, 170, 192], "displaystyl": [8, 45, 90, 115], "sum_": [8, 11, 45, 104, 105, 115, 121, 122], "w_j": [8, 45], "x_j": [8, 45], "f_j": [8, 45], "prod_": [8, 45, 90, 115], "k": [8, 11, 12, 21, 25, 28, 29, 30, 32, 33, 35, 45, 58, 73, 89, 99, 101, 104, 108, 109, 110, 111, 112, 113, 122, 124, 127, 146, 150, 166, 168, 174, 191, 193], "neq": [8, 45, 105, 121, 122], "x_k": [8, 45], "theori": [8, 45], "dx": [8, 28, 35, 54, 88, 91, 92, 94, 95, 96, 97, 100, 104, 106, 107, 108, 109, 112, 113, 114, 122, 124, 127, 129, 130, 133, 134, 135, 137, 139, 165, 166, 175, 191, 194], "1137": 8, "s0036144502417715": 8, "tupl": [8, 44, 45, 57, 72, 90, 92, 94, 95, 96, 97, 100, 106, 107, 108, 109, 110, 111, 114, 115, 120, 124, 127, 139, 190, 193, 198], "1darrai": [8, 45, 47, 48, 88, 89, 91, 92, 94, 95, 96, 99, 103, 104, 122, 124, 139], "scale": [8, 10, 12, 15, 16, 18, 19, 21, 25, 28, 29, 30, 32, 35, 45, 53, 91, 92, 94, 95, 96, 97, 122, 191, 197], "getinterpolationmatrix": [8, 45], "vec": [8, 16, 19, 45, 86, 88, 91, 92, 99, 100, 101, 102, 103, 107, 108, 109, 112, 113, 114, 120, 123, 124, 125, 127, 139], "tau_m": [8, 45], "p_": [8, 45], "inter": [8, 45, 122], "pinter": [8, 45], "2darrai": [8, 45, 101, 122, 123], "row": [8, 45, 65, 67, 73, 74, 107, 150], "column": [8, 45, 73, 107, 150, 167, 168, 191], "cute": 8, "pictur": [8, 12, 18, 21, 36], "cat": 8, "coverag": 9, "flatten": [9, 48], "steep": 9, "curv": 9, "eight": 9, "briefli": [9, 198], "discuss": [9, 196], "along": [9, 13, 122], "highlight": 9, "shown": [9, 12, 16], "ye": [9, 54], "jupyt": [9, 15], "notebook": [9, 15], "awesom": [9, 39], "statist": [9, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 44, 57, 59, 62, 63, 91, 172, 173, 174, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 194, 195, 196, 197, 198], "gather": [9, 16, 44, 122, 166, 168, 174, 175, 184, 191, 193, 194, 196, 198], "medium": 9, "group": 9, "bori": [9, 12, 122, 146, 193, 194], "becom": [9, 11, 18, 65, 73, 105, 121, 196], "evolv": 9, "proper": 9, "suppos": [9, 196, 198], "focuss": 9, "beyond": [9, 35, 194], "basi": [9, 12, 101], "present": [9, 41, 178, 194], "readm": 9, "intent": 9, "content": 9, "conform": 9, "attempt": 9, "fast": [9, 88, 89, 94, 95, 96, 97, 103, 110, 120, 122, 150], "wave": [9, 88, 89, 103, 106, 107, 150, 165, 166, 191], "rdc": 9, "ration": 9, "asymptot": 9, "fastest": 9, "bayreuth": 9, "modal": 9, "system": [9, 11, 15, 18, 32, 36, 73, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141, 144, 145, 167, 168, 191, 193, 197], "differenti": [9, 13, 15, 75, 98, 99, 101, 102, 108, 112, 113, 118, 119, 123, 127, 139, 145], "algebra": 9, "helper": [9, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 38, 41, 44, 62, 63, 99, 107, 109, 111, 122, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 193, 194, 195, 196, 197, 198], "tabl": [9, 39, 41], "search": 9, "materi": 10, "scienc": [10, 198], "paraphas": 10, "partner": 10, "flexibl": 10, "run_simple_forcing_verif": 10, "2d": [10, 11, 16, 33, 65, 74, 90, 92, 100, 114, 115, 160, 186, 197], "against": [10, 34], "known": [10, 11, 13, 42, 94, 95, 119, 122], "circl": [10, 91, 92, 94, 95, 96, 97], "shrink": [10, 167, 168, 191], "drive": [10, 91, 96, 97, 198], "vanish": [10, 73], "numer": [10, 11, 12, 18, 33, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 123, 124, 125, 126, 127, 140, 141, 145], "scheme": [10, 11, 33, 34, 35, 65, 66, 73, 74, 100, 143, 144, 145, 146, 195, 198], "constant": [10, 73, 92, 94, 95, 105, 111, 121, 122, 146, 195, 198], "dw": [10, 91, 96, 97], "radiu": [10, 17, 33, 35, 91, 92, 94, 95, 96, 97], "stai": [10, 101], "run_temp_forcing_verif": 10, "temperatur": [10, 119, 124], "run_temp_forcing_refer": 10, "These": [10, 15, 35, 36, 42, 144, 145], "serial": [10, 15, 18, 63, 72, 82, 84, 189, 195, 196, 197, 198], "mimick": 10, "larger": [10, 191, 197], "hpc": [10, 36], "machin": [10, 11, 16, 18, 196], "allencahn_monitor_and_dump": 10, "radii": 10, "dump": [10, 12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 41], "o": [10, 12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 166, 168, 184, 188, 189, 191, 196, 198], "allencahn_monitor": 10, "allencahn_dump": 10, "visual": [10, 16, 19, 28, 29, 30, 33, 35, 36, 59, 166, 168, 188, 191], "turn": [10, 194], "field": [10, 13, 44, 81, 85, 122, 173, 178, 193, 194], "png": [10, 12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 59, 166, 168, 188, 189, 191, 198], "visualize_temp": 10, "movi": 10, "run_pysc_ac": 10, "ex": [10, 36], "jobscript": 10, "jureca": [10, 36], "allencahn_mpifft": [10, 87], "problem_class": [10, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 46, 48, 56, 60, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "allencahn_temp_mpifft": [10, 87], "thesi": 11, "suffic": [11, 66], "misc": 11, "hookclass_da": 11, "linear_plot": 11, "previous": 11, "npy": 11, "axi": [11, 122, 166, 168, 191], "loglog_plot": 11, "logarithm": 11, "commonli": 11, "semilogy_plot": 11, "y": [11, 96, 97, 98, 109, 114, 117, 166, 168, 191], "simple_da": 11, "analyt": [11, 47, 88, 118, 165, 166, 167, 168, 191], "pendulum": 11, "veri": [11, 12, 13, 14, 16, 19, 34, 48, 102, 144, 171, 173, 191, 192, 193, 195], "solvabl": 11, "synchronous_machin": 11, "attach": [11, 193], "infinit": 11, "bu": 11, "undergo": 11, "torqu": 11, "disturb": 11, "transistor_amplifi": 11, "transistor": 11, "amplifi": 11, "world": [11, 187, 197], "situat": [11, 194], "run_convergence_test": 11, "mention": [11, 15, 33], "run_iteration_test": 11, "behaviour": [11, 66, 119, 143], "residu": [11, 33, 41, 51, 59, 65, 66, 68, 73, 76, 107, 109, 149, 151, 152, 170, 171, 172, 173, 185, 188, 189, 192, 193, 194, 197], 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25, 32], "plot_help": [12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 52], "plt_helper": [12, 16, 19, 21, 25, 28, 29, 30, 32, 35], "stats_help": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 52, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 193, 194, 195, 196, 197, 198], "get_sort": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 52, 57, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 193, 194, 195, 196, 197, 198], "filter_stat": [12, 21, 25, 32, 52, 57, 172, 193], "controller_class": [12, 16, 19, 21, 25, 26, 28, 29, 30, 32, 34, 35, 60, 171, 172, 173, 174, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "harmonicoscil": [12, 25, 87], "harmonic_oscil": [12, 25, 87, 111], "henonheil": [12, 25, 87], "henon_heil": [12, 25, 87, 117], "sweeper_class": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 46, 60, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "transfer_class": [12, 21, 25, 26, 27, 32, 34, 60, 175, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198], "transferparticles_nocoars": [12, 21, 25, 32, 155, 178, 194], "particles_to_particl": [12, 21, 25, 32, 155, 164, 178, 194], "setup_harmon": [12, 25], "everyth": [12, 21, 25, 32, 39, 169, 176, 192, 194], "dict": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 40, 41, 42, 44, 50, 56, 57, 59, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 90, 99, 104, 119, 122, 139, 166, 169, 170, 171, 173, 174, 175, 176, 177, 178, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "controller_param": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 41, 62, 63, 171, 172, 173, 174, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "level_param": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 46, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "restol": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "1e": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 90, 91, 92, 98, 99, 100, 102, 106, 107, 109, 110, 114, 115, 118, 119, 120, 124, 126, 139, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "sweeper_param": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 46, 65, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "num_nod": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 39, 47, 65, 144, 145, 167, 168, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "initial_guess": [12, 16, 19, 21, 25, 26, 27, 32, 34, 144, 145, 171, 173, 186, 187, 190, 192, 193, 197, 198], "zero": [12, 16, 19, 21, 25, 26, 27, 29, 30, 32, 34, 35, 48, 73, 99, 101, 124, 165, 166, 167, 168, 169, 170, 171, 172, 175, 176, 177, 179, 180, 182, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "problem_param": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 46, 166, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "amp": [12, 25, 111], "step_param": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "maxit": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "50": [12, 16, 19, 21, 25, 26, 27, 28, 32, 34, 35, 127, 172, 178, 180, 181, 182, 183, 184, 186, 187, 188, 189, 190, 193, 194, 195, 196, 197, 198], "hook_class": [12, 21, 25, 28, 32, 35, 171, 173, 174, 178, 190, 192, 193, 194, 198], "logger_level": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 65, 171, 172, 173, 174, 177, 178, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "fill": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 51, 122, 143, 144, 149, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "easi": [12, 16, 19, 21, 25, 26, 27, 28, 32, 34, 35, 169, 170, 171, 172, 173, 174, 176, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "hierarchi": [12, 21, 25, 28, 32, 35, 62, 63, 149, 170, 171, 172, 173, 174, 176, 178, 179, 185, 192, 193, 197], "space_transfer_class": [12, 16, 19, 21, 25, 26, 27, 32, 34, 38, 50, 156, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198], "setup_henonheil": [12, 25], "run_simul": [12, 21, 25, 32, 172, 174, 186, 190, 193, 197, 198], "prob": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 46, 107, 109, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 176, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "arg": [12, 16, 19, 21, 25, 26, 27, 28, 32, 34, 35, 48, 70, 90, 165, 166, 167, 168, 170, 182, 184, 185, 186, 191, 192, 196, 197], "str": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 40, 41, 42, 45, 47, 51, 53, 54, 55, 57, 59, 65, 66, 69, 72, 73, 74, 75, 90, 94, 95, 96, 97, 108, 112, 113, 115, 124, 127, 139, 143, 149, 152, 175, 184, 185, 187, 194, 196, 197], "t0": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 41, 62, 63, 108, 112, 113, 167, 168, 171, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "tend": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 41, 42, 62, 63, 67, 73, 78, 79, 167, 168, 171, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "num_proc": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 62, 63, 171, 172, 173, 174, 177, 178, 179, 180, 181, 182, 184, 185, 186, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "maxmeanit": [12, 25, 32], "elif": [12, 16, 19, 25, 26, 27, 28, 29, 30, 32, 34, 35, 185, 190, 197, 198], "instanti": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 41, 42, 48, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 165, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "finest": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 50, 62, 63, 66, 72, 73, 78, 171, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "uinit": 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30, 32, 34, 35, 41, 50, 62, 63, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 106, 107, 108, 109, 110, 111, 112, 113, 114, 118, 119, 120, 122, 123, 124, 125, 126, 127, 131, 137, 139, 140, 141, 167, 168, 171, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "filter": [12, 16, 19, 21, 25, 27, 28, 29, 30, 32, 34, 35, 57, 172, 173, 174, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 193, 195, 196, 197, 198], "iter_count": [12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 172, 180, 181, 182, 184, 185, 186, 187, 188, 190, 193, 195, 196, 197, 198], "niter": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 48, 170, 172, 177, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "sortbi": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 57, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 193, 194, 195, 196, 197, 198], "item": [12, 16, 19, 21, 25, 27, 28, 32, 34, 35, 57, 172, 173, 174, 178, 180, 181, 182, 184, 185, 186, 187, 188, 190, 193, 194, 195, 196, 197, 198], "2f": [12, 16, 19, 21, 25, 28, 32, 35, 170, 172, 175, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "2i": [12, 16, 19, 21, 25, 28, 32, 35, 166, 168, 170, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 189, 191, 192, 193, 194, 195, 196, 197, 198], "mean": [12, 13, 14, 15, 16, 18, 19, 21, 25, 28, 32, 35, 72, 73, 79, 99, 101, 114, 124, 149, 180, 181, 185, 186, 187, 190, 195, 197, 198], "rang": [12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 99, 107, 124, 165, 166, 168, 175, 176, 179, 180, 181, 185, 186, 187, 190, 191, 194, 195, 197, 198], "ptp": [12, 16, 19, 21, 25, 28, 32, 35, 180, 181, 185, 186, 187, 195, 197], "max": [12, 16, 19, 21, 25, 28, 32, 35, 68, 90, 115, 166, 168, 180, 181, 185, 186, 187, 188, 191, 195, 197, 198], "min": [12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 166, 168, 176, 180, 181, 185, 186, 187, 188, 191, 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182, 189, 190, 192, 194, 195, 196, 198], "imex_1st_ord": [16, 19, 142, 151, 152, 170, 171, 172, 179, 180, 185, 186, 187, 190, 192, 193, 195, 197, 198], "multi_implicit": [16, 19, 142], "setup_paramet": [16, 19], "relev": [16, 19, 42, 192, 193], "nsweep": [16, 19, 26, 27, 34, 146, 150, 171, 173, 186, 187, 190, 192, 193, 197, 198], "q1": [16, 19, 153], "lu": [16, 19, 26, 27, 28, 29, 34, 35, 169, 176, 177, 180, 181, 182, 186, 187, 189, 190, 192, 194, 195, 196, 197, 198], "q2": [16, 19, 153], "qi": [16, 19, 26, 27, 28, 29, 30, 34, 35, 144, 145, 148, 150, 169, 171, 173, 176, 177, 180, 181, 182, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "nu": [16, 19, 26, 27, 28, 29, 30, 34, 35, 89, 92, 94, 95, 106, 107, 112, 113, 114, 115, 127, 165, 166, 167, 168, 169, 170, 171, 172, 175, 176, 177, 179, 180, 182, 185, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "nvar": [16, 19, 26, 27, 28, 29, 30, 34, 35, 88, 89, 90, 91, 92, 94, 95, 96, 97, 100, 106, 107, 109, 110, 115, 120, 124, 139, 165, 166, 167, 168, 169, 170, 171, 172, 175, 176, 177, 179, 180, 181, 182, 186, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "2049": [16, 19], "lambda0": [16, 19, 28, 29, 30, 35, 106, 107], "interv": [16, 19, 28, 29, 30, 35, 39, 45, 46, 73, 91, 106, 107, 122, 146, 147, 148, 149, 150, 151, 152, 153, 154, 167, 168, 170, 172, 191, 192, 193], "nlsol_tol": [16, 19, 107, 109], "nlsol_maxit": [16, 19, 107, 109], "lsol_tol": [16, 19, 107, 109], "lsol_maxit": [16, 19, 107, 109], "space_transfer_param": [16, 19, 26, 27, 34, 38, 49, 50, 156, 175, 176, 177, 179, 180, 181, 182, 187, 189, 190, 194, 195, 196, 197, 198], "finter": [16, 19, 178, 185, 194, 197], "mesh_to_mesh_petsc_dmda": [16, 19, 155, 163, 187, 197], "run_sdc_vari": [16, 19], "bool": [16, 19, 39, 41, 42, 44, 46, 54, 57, 58, 65, 66, 67, 68, 69, 70, 73, 74, 75, 78, 91, 96, 97, 99, 102, 105, 106, 110, 118, 120, 121, 124, 126, 140, 149, 151, 182, 185, 186, 196, 197], "nor": [16, 19], "incomplet": [16, 19], "stuff": [16, 19, 42, 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"our-pledge"]], "Our Standards": [[1, "our-standards"]], "Enforcement Responsibilities": [[1, "enforcement-responsibilities"]], "Scope": [[1, "scope"]], "Enforcement": [[1, "enforcement"]], "Enforcement Guidelines": [[1, "enforcement-guidelines"]], "1. Correction": [[1, "correction"]], "2. Warning": [[1, "warning"]], "3. Temporary Ban": [[1, "temporary-ban"]], "4. Permanent Ban": [[1, "permanent-ban"]], "Attribution": [[1, "attribution"]], "How to contribute to pySDC": [[2, "how-to-contribute-to-pysdc"]], "Welcome to pySDC!": [[3, "welcome-to-pysdc"], [9, "welcome-to-pysdc"]], "Features": [[3, "features"], [9, "features"]], "Getting started": [[3, "getting-started"], [9, "getting-started"]], "How to cite": [[3, "how-to-cite"], [9, "how-to-cite"]], "Contributing": [[3, "contributing"], [9, "contributing"]], "Acknowledgements": [[3, "acknowledgements"], [9, "acknowledgements"]], "Recommendations for pull requests": [[4, "recommendations-for-pull-requests"]], "Contributing to the main branch": [[4, "contributing-to-the-main-branch"]], "Release development branches": [[4, "release-development-branches"]], "Feature development branches": [[4, "feature-development-branches"]], "Continuous Integration in pySDC": [[5, "continuous-integration-in-pysdc"]], "Code linting": [[5, "code-linting"]], "Code testing": [[5, "code-testing"]], "Code coverage": [[5, "code-coverage"]], "Coverage exceptions": [[5, "coverage-exceptions"]], "Documentation generation": [[5, "documentation-generation"]], "Naming conventions in pySDC": [[6, "naming-conventions-in-pysdc"]], "First definitions": [[6, "first-definitions"]], "Packages and modules names": [[6, "packages-and-modules-names"]], "Class names": [[6, "class-names"]], "Function and variables names": [[6, "function-and-variables-names"]], "Private and public attributes": [[6, "private-and-public-attributes"]], "Constants": [[6, "constants"]], "Custom implementation guidelines": [[7, "custom-implementation-guidelines"]], "Implementing a custom problem class": [[7, "implementing-a-custom-problem-class"]], "Documenting Code": [[8, "documenting-code"]], "Tests": [[9, "tests"], [15, "tests"]], "User Guide": [[9, "user-guide"]], "Tutorial": [[9, "tutorial"]], "Playgrounds": [[9, "playgrounds"]], "Projects": [[9, "projects"]], "API documentation": [[9, "api-documentation"]], "Allen-Cahn problems from Bayreuth": [[10, "allen-cahn-problems-from-bayreuth"]], "Verification": [[10, "verification"]], "Benchmark": [[10, "benchmark"]], "Application": [[10, "application"]], "Further/related files": [[10, "further-related-files"]], "Solving differential algebraic equations with SDC": [[11, "solving-differential-algebraic-equations-with-sdc"]], "Project overview": [[11, "project-overview"]], "Theoretical details": [[11, "theoretical-details"]], "Second-order Problems": [[12, "second-order-problems"]], "Simple problems": [[12, "simple-problems"]], "Solar system problem": [[12, "solar-system-problem"]], "Fermi-Pasta-Ulam-Tsingou problem": [[12, "fermi-pasta-ulam-tsingou-problem"]], "Parallel-in-time simulation for multi-modal energy systems": [[13, "parallel-in-time-simulation-for-multi-modal-energy-systems"]], "What are switching processes in power systems?": [[13, "what-are-switching-processes-in-power-systems"]], "Pi-line": [[13, "pi-line"]], "Buck converter": [[13, "buck-converter"]], "Battery drain model": [[13, "battery-drain-model"]], "RDC: Rational Deferred Corrections": [[14, "rdc-rational-deferred-corrections"]], "Testing RDC convergence": [[14, "testing-rdc-convergence"]], "Multi-level RDC and PFASST with RDC": [[14, "multi-level-rdc-and-pfasst-with-rdc"]], "Resilience in SDC": [[15, "resilience-in-sdc"]], "What is the fastest SDC variant?": [[16, "what-is-the-fastest-sdc-variant"]], "Fisher and Gray-Scott equations": [[16, "fisher-and-gray-scott-equations"]], "Asymptotic convergence of PFASST": [[17, "asymptotic-convergence-of-pfasst"]], "Organisation of the project": [[17, "organisation-of-the-project"]], "Compression in pySDC": [[18, "compression-in-pysdc"]], "Introduction": [[18, "introduction"]], "Methods": [[18, "methods"]], "Proof of Concept": [[18, "proof-of-concept"]], "Fast-Wave-Slow-Wave SDC": [[33, "fast-wave-slow-wave-sdc"]], "Theoretical results": [[33, "theoretical-results"]], "Acoustic-advection example": [[33, "acoustic-advection-example"]], "Boussinesq example": [[33, "boussinesq-example"]], "Matrix-based versions of PFASST": [[34, "matrix-based-versions-of-pfasst"]], "Matrix-based PFASST": [[34, "matrix-based-pfasst"]], "Propagator-based PFASST": [[34, "propagator-based-pfasst"]], "Attempts to parallelize SDC": [[35, "attempts-to-parallelize-sdc"]], "Different preconditioners for SDC": [[35, "different-preconditioners-for-sdc"]], "Node-parallel SDC with MPI": [[35, "node-parallel-sdc-with-mpi"], [35, "id1"]], "Simplified Newton for nonlinear problems": [[35, "simplified-newton-for-nonlinear-problems"]], "Performance analysis of pySDC": [[36, "performance-analysis-of-pysdc"]], "Python codes": [[36, "python-codes"]], "Jobscripts": [[36, "jobscripts"]], "Results": [[36, "results"]], "core package": [[37, "core-package"]], "Submodules": [[37, "submodules"], [52, "submodules"], [61, "submodules"], [64, "submodules"], [81, "submodules"], [87, "submodules"], [128, "submodules"], [132, "submodules"], [142, "submodules"], [155, 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"module-implementations.convergence_controller_classes.basic_restarting"]], "implementations.convergence_controller_classes.check_convergence module": [[68, "module-implementations.convergence_controller_classes.check_convergence"]], "implementations.convergence_controller_classes.check_iteration_estimator module": [[69, "module-implementations.convergence_controller_classes.check_iteration_estimator"]], "implementations.convergence_controller_classes.crash module": [[70, "module-implementations.convergence_controller_classes.crash"]], "implementations.convergence_controller_classes.estimate_contraction_factor module": [[71, "module-implementations.convergence_controller_classes.estimate_contraction_factor"]], "implementations.convergence_controller_classes.estimate_embedded_error module": [[72, "module-implementations.convergence_controller_classes.estimate_embedded_error"]], "implementations.convergence_controller_classes.estimate_extrapolation_error module": [[73, 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"implementations.problem_classes.AllenCahn_2D_FFT module": [[94, "module-implementations.problem_classes.AllenCahn_2D_FFT"]], "implementations.problem_classes.AllenCahn_2D_FFT_gpu module": [[95, "module-implementations.problem_classes.AllenCahn_2D_FFT_gpu"]], "implementations.problem_classes.AllenCahn_MPIFFT module": [[96, "module-implementations.problem_classes.AllenCahn_MPIFFT"]], "implementations.problem_classes.AllenCahn_Temp_MPIFFT module": [[97, "module-implementations.problem_classes.AllenCahn_Temp_MPIFFT"]], "implementations.problem_classes.Auzinger_implicit module": [[98, "module-implementations.problem_classes.Auzinger_implicit"]], "implementations.problem_classes.Battery module": [[99, "module-implementations.problem_classes.Battery"]], "implementations.problem_classes.Boussinesq_2D_FD_imex module": [[100, "module-implementations.problem_classes.Boussinesq_2D_FD_imex"]], "implementations.problem_classes.BuckConverter module": [[101, 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"implementations.problem_classes.acoustic_helpers.buildWave1DMatrix module": [[130, "module-implementations.problem_classes.acoustic_helpers.buildWave1DMatrix"]], "implementations.problem_classes.acoustic_helpers.standard_integrators module": [[131, "module-implementations.problem_classes.acoustic_helpers.standard_integrators"]], "implementations.problem_classes.boussinesq_helpers package": [[132, "implementations-problem-classes-boussinesq-helpers-package"]], "implementations.problem_classes.boussinesq_helpers.build2DFDMatrix module": [[133, "module-implementations.problem_classes.boussinesq_helpers.build2DFDMatrix"]], "implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix module": [[134, "module-implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix"]], "implementations.problem_classes.boussinesq_helpers.buildFDMatrix module": [[135, "module-implementations.problem_classes.boussinesq_helpers.buildFDMatrix"]], 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check": [[191, "part-b-spatial-accuracy-check"]], "Part C: Collocation problem setup": [[191, "part-c-collocation-problem-setup"]], "Part D: Collocation accuracy test": [[191, "part-d-collocation-accuracy-test"]], "Step-2: Data structures and my first sweeper": [[192, "step-2-data-structures-and-my-first-sweeper"]], "Part A: Step data structure": [[192, "part-a-step-data-structure"]], "Part B: My first sweeper": [[192, "part-b-my-first-sweeper"]], "Part C: Using pySDC\u2019s frontend": [[192, "part-c-using-pysdc-s-frontend"]], "Step-3: Statistics and a new sweeper": [[193, "step-3-statistics-and-a-new-sweeper"]], "Part A: Getting statistics": [[193, "part-a-getting-statistics"]], "Part B: Adding statistics": [[193, "part-b-adding-statistics"]], "Part C: Studying collocation node types": [[193, "part-c-studying-collocation-node-types"]], "Step-4: Multilevel SDC": [[194, "step-4-multilevel-sdc"]], "Part A: Spatial transfer operators": [[194, "part-a-spatial-transfer-operators"]], "Part 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"core.Errors.DataError"]], "parametererror": [[43, "core.Errors.ParameterError"]], "problemerror": [[43, "core.Errors.ProblemError"]], "readonlyerror": [[43, "core.Errors.ReadOnlyError"]], "transfererror": [[43, "core.Errors.TransferError"]], "unlockerror": [[43, "core.Errors.UnlockError"]], "core.errors": [[43, "module-core.Errors"]], "entry (class in core.hooks)": [[44, "core.Hooks.Entry"]], "__num_restarts (hooks attribute)": [[44, "core.Hooks.hooks.__num_restarts"]], "__stats (hooks attribute)": [[44, "core.Hooks.hooks.__stats"]], "add_to_stats() (hooks method)": [[44, "core.Hooks.hooks.add_to_stats"]], "core.hooks": [[44, "module-core.Hooks"]], "entry (hooks attribute)": [[44, "core.Hooks.hooks.entry"], [44, "id0"]], "hooks (class in core.hooks)": [[44, "core.Hooks.hooks"]], "increment_stats() (hooks method)": [[44, "core.Hooks.hooks.increment_stats"]], "iter (entry attribute)": [[44, "core.Hooks.Entry.iter"]], "level (entry attribute)": [[44, "core.Hooks.Entry.level"]], "logger (hooks attribute)": [[44, "core.Hooks.hooks.logger"]], "meta_data (hooks attribute)": [[44, "core.Hooks.hooks.meta_data"]], "num_restarts (entry attribute)": [[44, "core.Hooks.Entry.num_restarts"]], "post_comm() (hooks method)": [[44, "core.Hooks.hooks.post_comm"]], "post_iteration() (hooks method)": [[44, "core.Hooks.hooks.post_iteration"]], "post_predict() (hooks method)": [[44, "core.Hooks.hooks.post_predict"]], "post_run() (hooks method)": [[44, "core.Hooks.hooks.post_run"]], "post_setup() (hooks method)": [[44, "core.Hooks.hooks.post_setup"]], "post_step() (hooks method)": [[44, "core.Hooks.hooks.post_step"]], "post_sweep() (hooks method)": [[44, "core.Hooks.hooks.post_sweep"]], "pre_comm() (hooks method)": [[44, "core.Hooks.hooks.pre_comm"]], "pre_iteration() (hooks method)": [[44, "core.Hooks.hooks.pre_iteration"]], "pre_predict() (hooks method)": [[44, "core.Hooks.hooks.pre_predict"]], "pre_run() (hooks method)": [[44, "core.Hooks.hooks.pre_run"]], "pre_setup() (hooks method)": 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"core.Lagrange.LagrangeApproximation.getIntegrationMatrix"]], "getinterpolationmatrix() (lagrangeapproximation method)": [[45, "core.Lagrange.LagrangeApproximation.getInterpolationMatrix"]], "n (lagrangeapproximation property)": [[45, "core.Lagrange.LagrangeApproximation.n"]], "points (lagrangeapproximation attribute)": [[45, "core.Lagrange.LagrangeApproximation.points"]], "weights (lagrangeapproximation attribute)": [[45, "core.Lagrange.LagrangeApproximation.weights"]], "core.level": [[46, "module-core.Level"]], "dt (level property)": [[46, "core.Level.level.dt"]], "f (level attribute)": [[46, "core.Level.level.f"]], "fold (level attribute)": [[46, "core.Level.level.fold"]], "level (class in core.level)": [[46, "core.Level.level"]], "level_index (level attribute)": [[46, "core.Level.level.level_index"]], "params (level attribute)": [[46, "core.Level.level.params"]], "prob (level property)": [[46, "core.Level.level.prob"]], "reset_level() (level method)": [[46, "core.Level.level.reset_level"]], "status (level attribute)": [[46, "core.Level.level.status"]], "sweep (level property)": [[46, "core.Level.level.sweep"]], "tag (level property)": [[46, "core.Level.level.tag"]], "tau (level attribute)": [[46, "core.Level.level.tau"]], "time (level property)": [[46, "core.Level.level.time"]], "u (level attribute)": [[46, "core.Level.level.u"]], "uend (level attribute)": [[46, "core.Level.level.uend"]], "uold (level attribute)": [[46, "core.Level.level.uold"]], "nodeserror": [[47, "core.Nodes.NodesError"]], "nodesgenerator (class in core.nodes)": [[47, "core.Nodes.NodesGenerator"]], "core.nodes": [[47, "module-core.Nodes"]], "evalorthogpoly() (nodesgenerator method)": [[47, "core.Nodes.NodesGenerator.evalOrthogPoly"]], "getnodes() (nodesgenerator method)": [[47, "core.Nodes.NodesGenerator.getNodes"]], "getorthogpolycoefficients() (nodesgenerator method)": [[47, "core.Nodes.NodesGenerator.getOrthogPolyCoefficients"]], "gettridiagcoefficients() (nodesgenerator method)": [[47, "core.Nodes.NodesGenerator.getTridiagCoefficients"]], "node_type (nodesgenerator attribute)": [[47, "core.Nodes.NodesGenerator.node_type"]], "quad_type (nodesgenerator attribute)": [[47, "core.Nodes.NodesGenerator.quad_type"]], "workcounter (class in core.problem)": [[48, "core.Problem.WorkCounter"]], "apply_mass_matrix() (ptype method)": [[48, "core.Problem.ptype.apply_mass_matrix"]], "core.problem": [[48, "module-core.Problem"]], "decrement() (workcounter method)": [[48, "core.Problem.WorkCounter.decrement"]], "dtype_f (ptype attribute)": [[48, "core.Problem.ptype.dtype_f"]], "dtype_u (ptype attribute)": [[48, "core.Problem.ptype.dtype_u"]], "eval_f() (ptype method)": [[48, "core.Problem.ptype.eval_f"]], "f_init (ptype property)": [[48, "core.Problem.ptype.f_init"]], "generate_scipy_reference_solution() (ptype method)": [[48, "core.Problem.ptype.generate_scipy_reference_solution"]], "get_default_sweeper_class() (ptype class method)": [[48, "core.Problem.ptype.get_default_sweeper_class"]], "logger (ptype attribute)": [[48, "core.Problem.ptype.logger"], [48, "id0"]], "ptype (class in core.problem)": [[48, "core.Problem.ptype"]], "u_init (ptype property)": [[48, "core.Problem.ptype.u_init"]], "coarse_prob (space_transfer attribute)": [[49, "core.SpaceTransfer.space_transfer.coarse_prob"]], "core.spacetransfer": [[49, "module-core.SpaceTransfer"]], "fine_prob (space_transfer attribute)": [[49, "core.SpaceTransfer.space_transfer.fine_prob"]], "logger (space_transfer attribute)": [[49, "core.SpaceTransfer.space_transfer.logger"]], "params (space_transfer attribute)": [[49, "core.SpaceTransfer.space_transfer.params"]], "prolong() (space_transfer method)": [[49, "core.SpaceTransfer.space_transfer.prolong"]], "restrict() (space_transfer method)": [[49, "core.SpaceTransfer.space_transfer.restrict"]], "space_transfer (class in core.spacetransfer)": [[49, "core.SpaceTransfer.space_transfer"]], "connect_levels() (step method)": [[50, "core.Step.step.connect_levels"]], "core.step": [[50, "module-core.Step"]], "dt (step property)": [[50, "core.Step.step.dt"]], "init_step() (step method)": [[50, "core.Step.step.init_step"]], "levels (step attribute)": [[50, "core.Step.step.levels"]], "logger (step attribute)": [[50, "core.Step.step.logger"]], "next (step property)": [[50, "core.Step.step.next"]], "params (step attribute)": [[50, "core.Step.step.params"]], "prev (step property)": [[50, "core.Step.step.prev"]], "reset_step() (step method)": [[50, "core.Step.step.reset_step"]], "status (step attribute)": [[50, "core.Step.step.status"]], "step (class in core.step)": [[50, "core.Step.step"]], "time (step property)": [[50, "core.Step.step.time"]], "transfer() (step method)": [[50, "core.Step.step.transfer"]], "coll (sweeper attribute)": [[51, "core.Sweeper.sweeper.coll"]], "compute_end_point() (sweeper method)": [[51, "core.Sweeper.sweeper.compute_end_point"]], "compute_residual() (sweeper method)": [[51, "core.Sweeper.sweeper.compute_residual"]], "core.sweeper": [[51, "module-core.Sweeper"]], "get_qdelta_explicit() (sweeper method)": [[51, "core.Sweeper.sweeper.get_Qdelta_explicit"]], "get_qdelta_implicit() (sweeper method)": [[51, "core.Sweeper.sweeper.get_Qdelta_implicit"]], "integrate() (sweeper method)": [[51, "core.Sweeper.sweeper.integrate"]], "level (sweeper property)": [[51, "core.Sweeper.sweeper.level"]], "logger (sweeper attribute)": [[51, "core.Sweeper.sweeper.logger"]], "params (sweeper attribute)": [[51, "core.Sweeper.sweeper.params"]], "predict() (sweeper method)": [[51, "core.Sweeper.sweeper.predict"]], "rank (sweeper property)": [[51, "core.Sweeper.sweeper.rank"]], "sweeper (class in core.sweeper)": [[51, "core.Sweeper.sweeper"]], "update_nodes() (sweeper method)": [[51, "core.Sweeper.sweeper.update_nodes"]], "helpers": [[52, "module-helpers"]], "figsize() (in module helpers.plot_helper)": [[53, "helpers.plot_helper.figsize"]], "figsize_by_journal() (in module 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"helpers.pysdc_helper.FrozenClass"]], "__isfrozen (frozenclass attribute)": [[55, "helpers.pysdc_helper.FrozenClass.__isfrozen"]], "get() (frozenclass method)": [[55, "helpers.pysdc_helper.FrozenClass.get"]], "helpers.pysdc_helper": [[55, "module-helpers.pysdc_helper"]], "generate_description() (in module helpers.setup_helper)": [[56, "helpers.setup_helper.generate_description"]], "helpers.setup_helper": [[56, "module-helpers.setup_helper"]], "filter_stats() (in module helpers.stats_helper)": [[57, "helpers.stats_helper.filter_stats"]], "get_list_of_types() (in module helpers.stats_helper)": [[57, "helpers.stats_helper.get_list_of_types"]], "get_sorted() (in module helpers.stats_helper)": [[57, "helpers.stats_helper.get_sorted"]], "helpers.stats_helper": [[57, "module-helpers.stats_helper"]], "sort_stats() (in module helpers.stats_helper)": [[57, "helpers.stats_helper.sort_stats"]], "border_padding() (in module helpers.transfer_helper)": [[58, 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"implementations.controller_classes": [[61, "module-implementations.controller_classes"]], "check_iteration_estimate() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.check_iteration_estimate"]], "controller_mpi (class in implementations.controller_classes.controller_mpi)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI"]], "default() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.default"]], "implementations.controller_classes.controller_mpi": [[62, "module-implementations.controller_classes.controller_MPI"]], "it_check() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.it_check"]], "it_coarse() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.it_coarse"]], "it_down() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.it_down"]], "it_fine() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.it_fine"]], "it_up() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.it_up"]], "pfasst() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.pfasst"]], "predict() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.predict"]], "recv() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.recv"]], "recv_full() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.recv_full"]], "restart_block() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.restart_block"]], "run() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.run"]], "send_full() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.send_full"]], "spread() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.spread"]], "wait_with_interrupt() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.wait_with_interrupt"]], "controller_nonmpi (class in implementations.controller_classes.controller_nonmpi)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI"]], "default() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.default"]], "implementations.controller_classes.controller_nonmpi": [[63, "module-implementations.controller_classes.controller_nonMPI"]], "it_check() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.it_check"]], "it_coarse() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.it_coarse"]], "it_down() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.it_down"]], "it_fine() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.it_fine"]], "it_up() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.it_up"]], "pfasst() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.pfasst"]], "predict() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.predict"]], "recv_full() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.recv_full"]], "restart_block() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.restart_block"]], "run() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.run"]], "send_full() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.send_full"]], "spread() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.spread"]], "implementations.convergence_controller_classes": [[64, "module-implementations.convergence_controller_classes"]], "adaptivecollocation (class in implementations.convergence_controller_classes.adaptive_collocation)": [[65, "implementations.convergence_controller_classes.adaptive_collocation.AdaptiveCollocation"]], "check_parameters() (adaptivecollocation method)": [[65, "implementations.convergence_controller_classes.adaptive_collocation.AdaptiveCollocation.check_parameters"]], "implementations.convergence_controller_classes.adaptive_collocation": [[65, "module-implementations.convergence_controller_classes.adaptive_collocation"]], "matmul() (adaptivecollocation method)": [[65, "implementations.convergence_controller_classes.adaptive_collocation.AdaptiveCollocation.matmul"]], "post_iteration_processing() (adaptivecollocation method)": [[65, "implementations.convergence_controller_classes.adaptive_collocation.AdaptiveCollocation.post_iteration_processing"]], "post_spread_processing() (adaptivecollocation method)": [[65, "implementations.convergence_controller_classes.adaptive_collocation.AdaptiveCollocation.post_spread_processing"]], "reset_status_variables() (adaptivecollocation method)": [[65, "implementations.convergence_controller_classes.adaptive_collocation.AdaptiveCollocation.reset_status_variables"]], "setup() (adaptivecollocation method)": 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(class in implementations.convergence_controller_classes.adaptivity)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityExtrapolationWithinQ"]], "adaptivityforconvergedcollocationproblems (class in implementations.convergence_controller_classes.adaptivity)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityForConvergedCollocationProblems"]], "adaptivitypolynomialerror (class in implementations.convergence_controller_classes.adaptivity)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityPolynomialError"]], "adaptivityrk (class in implementations.convergence_controller_classes.adaptivity)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityRK"]], "adaptivityresidual (class in implementations.convergence_controller_classes.adaptivity)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityResidual"]], "check_parameters() (adaptivity method)": [[66, "implementations.convergence_controller_classes.adaptivity.Adaptivity.check_parameters"]], "check_parameters() (adaptivitycollocation method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityCollocation.check_parameters"]], "check_parameters() (adaptivityresidual method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityResidual.check_parameters"]], "compute_optimal_step_size() (adaptivitybase method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityBase.compute_optimal_step_size"]], "dependencies() (adaptivity method)": [[66, "implementations.convergence_controller_classes.adaptivity.Adaptivity.dependencies"]], "dependencies() (adaptivitybase method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityBase.dependencies"]], "dependencies() (adaptivitycollocation method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityCollocation.dependencies"]], "dependencies() (adaptivityextrapolationwithinq method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityExtrapolationWithinQ.dependencies"]], "dependencies() (adaptivitypolynomialerror method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityPolynomialError.dependencies"]], "determine_restart() (adaptivitybase method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityBase.determine_restart"]], "determine_restart() (adaptivitycollocation method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityCollocation.determine_restart"]], "determine_restart() (adaptivityforconvergedcollocationproblems method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityForConvergedCollocationProblems.determine_restart"]], "get_convergence() (adaptivitycollocation method)": [[66, 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"implementations.problem_classes.PenningTrap_3D.penningtrap.u_exact"]], "u_init() (penningtrap method)": [[122, "implementations.problem_classes.PenningTrap_3D.penningtrap.u_init"]], "work_counter (penningtrap attribute)": [[122, "implementations.problem_classes.PenningTrap_3D.penningtrap.work_counter"]], "dtype_f (piline attribute)": [[123, "implementations.problem_classes.Piline.piline.dtype_f"]], "dtype_u (piline attribute)": [[123, "implementations.problem_classes.Piline.piline.dtype_u"]], "eval_f() (piline method)": [[123, "implementations.problem_classes.Piline.piline.eval_f"]], "implementations.problem_classes.piline": [[123, "module-implementations.problem_classes.Piline"]], "piline (class in implementations.problem_classes.piline)": [[123, "implementations.problem_classes.Piline.piline"]], "solve_system() (piline method)": [[123, "implementations.problem_classes.Piline.piline.solve_system"]], "u_exact() (piline method)": [[123, "implementations.problem_classes.Piline.piline.u_exact"]], "a (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.A"]], "id (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.Id"]], "quench (class in implementations.problem_classes.quench)": [[124, "implementations.problem_classes.Quench.Quench"]], "quenchimex (class in implementations.problem_classes.quench)": [[124, "implementations.problem_classes.Quench.QuenchIMEX"]], "dtype_f (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.dtype_f"]], "dtype_f (quenchimex attribute)": [[124, "implementations.problem_classes.Quench.QuenchIMEX.dtype_f"]], "dtype_u (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.dtype_u"]], "dx (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.dx"]], "eval_f() (quench method)": [[124, "implementations.problem_classes.Quench.Quench.eval_f"]], "eval_f() (quenchimex method)": [[124, "implementations.problem_classes.Quench.QuenchIMEX.eval_f"]], "eval_f_non_linear() (quench method)": [[124, "implementations.problem_classes.Quench.Quench.eval_f_non_linear"]], "get_non_linear_jacobian() (quench method)": [[124, "implementations.problem_classes.Quench.Quench.get_non_linear_Jacobian"]], "implementations.problem_classes.quench": [[124, "module-implementations.problem_classes.Quench"]], "leak (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.leak"]], "solve_system() (quench method)": [[124, "implementations.problem_classes.Quench.Quench.solve_system"]], "solve_system() (quenchimex method)": [[124, "implementations.problem_classes.Quench.QuenchIMEX.solve_system"]], "u_exact() (quench method)": [[124, "implementations.problem_classes.Quench.Quench.u_exact"]], "u_exact() (quenchimex method)": [[124, "implementations.problem_classes.Quench.QuenchIMEX.u_exact"]], "xv (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.xv"]], "a (testequation0d attribute)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d.A"]], "dtype_f (testequation0d attribute)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d.dtype_f"]], "dtype_u (testequation0d attribute)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d.dtype_u"]], "eval_f() (testequation0d method)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d.eval_f"]], "implementations.problem_classes.testequation_0d": [[125, "module-implementations.problem_classes.TestEquation_0D"]], "solve_system() (testequation0d method)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d.solve_system"]], "testequation0d (class in implementations.problem_classes.testequation_0d)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d"]], "u_exact() (testequation0d method)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d.u_exact"]], "dtype_f (vanderpol attribute)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol.dtype_f"]], "dtype_u (vanderpol attribute)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol.dtype_u"]], "eval_f() (vanderpol method)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol.eval_f"]], "implementations.problem_classes.van_der_pol_implicit": [[126, "module-implementations.problem_classes.Van_der_Pol_implicit"]], "solve_system() (vanderpol method)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol.solve_system"]], "u_exact() (vanderpol method)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol.u_exact"]], "vanderpol (class in implementations.problem_classes.van_der_pol_implicit)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol"]], "work_counters (vanderpol attribute)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol.work_counters"]], "k (fenics_vortex_2d attribute)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.K"]], "m (fenics_vortex_2d attribute)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.M"]], "v (fenics_vortex_2d attribute)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.V"]], "dtype_f (fenics_vortex_2d attribute)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.dtype_f"]], "dtype_u (fenics_vortex_2d attribute)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.dtype_u"]], "eval_f() (fenics_vortex_2d method)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.eval_f"]], "fenics_vortex_2d (class in implementations.problem_classes.vorticityvelocity_2d_fenics_periodic)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d"]], "implementations.problem_classes.vorticityvelocity_2d_fenics_periodic": [[127, "module-implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic"]], "solve_system() (fenics_vortex_2d method)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.solve_system"]], "u_exact() (fenics_vortex_2d method)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.u_exact"]], "implementations.problem_classes.acoustic_helpers": [[128, "module-implementations.problem_classes.acoustic_helpers"]], "getbcleft() (in module implementations.problem_classes.acoustic_helpers.buildfdmatrix)": [[129, "implementations.problem_classes.acoustic_helpers.buildFDMatrix.getBCLeft"]], "getbcright() (in module implementations.problem_classes.acoustic_helpers.buildfdmatrix)": [[129, "implementations.problem_classes.acoustic_helpers.buildFDMatrix.getBCRight"]], "gethorizontaldx() (in module implementations.problem_classes.acoustic_helpers.buildfdmatrix)": [[129, "implementations.problem_classes.acoustic_helpers.buildFDMatrix.getHorizontalDx"]], "getmatrix() (in module implementations.problem_classes.acoustic_helpers.buildfdmatrix)": [[129, "implementations.problem_classes.acoustic_helpers.buildFDMatrix.getMatrix"]], "implementations.problem_classes.acoustic_helpers.buildfdmatrix": [[129, "module-implementations.problem_classes.acoustic_helpers.buildFDMatrix"]], "getwave1dadvectionmatrix() (in module implementations.problem_classes.acoustic_helpers.buildwave1dmatrix)": [[130, "implementations.problem_classes.acoustic_helpers.buildWave1DMatrix.getWave1DAdvectionMatrix"]], "getwave1dmatrix() (in module implementations.problem_classes.acoustic_helpers.buildwave1dmatrix)": [[130, "implementations.problem_classes.acoustic_helpers.buildWave1DMatrix.getWave1DMatrix"]], "getwavebcleft() (in module implementations.problem_classes.acoustic_helpers.buildwave1dmatrix)": [[130, "implementations.problem_classes.acoustic_helpers.buildWave1DMatrix.getWaveBCLeft"]], "getwavebcright() (in module implementations.problem_classes.acoustic_helpers.buildwave1dmatrix)": [[130, "implementations.problem_classes.acoustic_helpers.buildWave1DMatrix.getWaveBCRight"]], "implementations.problem_classes.acoustic_helpers.buildwave1dmatrix": [[130, "module-implementations.problem_classes.acoustic_helpers.buildWave1DMatrix"]], "bdf2 (class in implementations.problem_classes.acoustic_helpers.standard_integrators)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.bdf2"]], "dirk (class in implementations.problem_classes.acoustic_helpers.standard_integrators)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.dirk"]], "f() (dirk method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.dirk.f"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.dirk.f"]], "f_fast() (rk_imex method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.rk_imex.f_fast"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.rk_imex.f_fast"]], "f_fast_solve() (rk_imex method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.rk_imex.f_fast_solve"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.rk_imex.f_fast_solve"]], "f_slow() (rk_imex method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.rk_imex.f_slow"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.rk_imex.f_slow"]], "f_solve() (dirk method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.dirk.f_solve"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.dirk.f_solve"]], "firsttimestep() (bdf2 method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.bdf2.firsttimestep"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.bdf2.firsttimestep"]], "implementations.problem_classes.acoustic_helpers.standard_integrators": [[131, "module-implementations.problem_classes.acoustic_helpers.standard_integrators"]], "rk_imex (class in implementations.problem_classes.acoustic_helpers.standard_integrators)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.rk_imex"]], "timestep() (bdf2 method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.bdf2.timestep"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.bdf2.timestep"]], "timestep() (dirk method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.dirk.timestep"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.dirk.timestep"]], "timestep() (rk_imex method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.rk_imex.timestep"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.rk_imex.timestep"]], "timestep() (trapezoidal method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.trapezoidal.timestep"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.trapezoidal.timestep"]], "trapezoidal (class in implementations.problem_classes.acoustic_helpers.standard_integrators)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.trapezoidal"]], "implementations.problem_classes.boussinesq_helpers": [[132, "module-implementations.problem_classes.boussinesq_helpers"]], "get2dmatrix() (in module implementations.problem_classes.boussinesq_helpers.build2dfdmatrix)": [[133, "implementations.problem_classes.boussinesq_helpers.build2DFDMatrix.get2DMatrix"]], "get2dmesh() (in module implementations.problem_classes.boussinesq_helpers.build2dfdmatrix)": [[133, "implementations.problem_classes.boussinesq_helpers.build2DFDMatrix.get2DMesh"]], "get2dupwindmatrix() (in module implementations.problem_classes.boussinesq_helpers.build2dfdmatrix)": [[133, "implementations.problem_classes.boussinesq_helpers.build2DFDMatrix.get2DUpwindMatrix"]], "getbchorizontal() (in module implementations.problem_classes.boussinesq_helpers.build2dfdmatrix)": [[133, "implementations.problem_classes.boussinesq_helpers.build2DFDMatrix.getBCHorizontal"]], "getbcvertical() (in module implementations.problem_classes.boussinesq_helpers.build2dfdmatrix)": [[133, "implementations.problem_classes.boussinesq_helpers.build2DFDMatrix.getBCVertical"]], "implementations.problem_classes.boussinesq_helpers.build2dfdmatrix": [[133, "module-implementations.problem_classes.boussinesq_helpers.build2DFDMatrix"]], "getboussinesq2dmatrix() (in module implementations.problem_classes.boussinesq_helpers.buildboussinesq2dmatrix)": [[134, "implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix.getBoussinesq2DMatrix"]], "getboussinesq2dupwindmatrix() (in module implementations.problem_classes.boussinesq_helpers.buildboussinesq2dmatrix)": [[134, "implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix.getBoussinesq2DUpwindMatrix"]], "getboussinesqbchorizontal() (in module implementations.problem_classes.boussinesq_helpers.buildboussinesq2dmatrix)": [[134, "implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix.getBoussinesqBCHorizontal"]], "getboussinesqbcvertical() (in module implementations.problem_classes.boussinesq_helpers.buildboussinesq2dmatrix)": [[134, "implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix.getBoussinesqBCVertical"]], "implementations.problem_classes.boussinesq_helpers.buildboussinesq2dmatrix": [[134, "module-implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix"]], "getbcleft() (in module implementations.problem_classes.boussinesq_helpers.buildfdmatrix)": [[135, "implementations.problem_classes.boussinesq_helpers.buildFDMatrix.getBCLeft"]], "getbcright() (in module implementations.problem_classes.boussinesq_helpers.buildfdmatrix)": [[135, "implementations.problem_classes.boussinesq_helpers.buildFDMatrix.getBCRight"]], "getmatrix() (in module implementations.problem_classes.boussinesq_helpers.buildfdmatrix)": [[135, "implementations.problem_classes.boussinesq_helpers.buildFDMatrix.getMatrix"]], "getupwindmatrix() (in module implementations.problem_classes.boussinesq_helpers.buildfdmatrix)": [[135, "implementations.problem_classes.boussinesq_helpers.buildFDMatrix.getUpwindMatrix"]], "implementations.problem_classes.boussinesq_helpers.buildfdmatrix": [[135, "module-implementations.problem_classes.boussinesq_helpers.buildFDMatrix"]], "callback (class in implementations.problem_classes.boussinesq_helpers.helper_classes)": [[136, "implementations.problem_classes.boussinesq_helpers.helper_classes.Callback"]], "add() (logging method)": [[136, "implementations.problem_classes.boussinesq_helpers.helper_classes.logging.add"]], "getcounter() (callback method)": [[136, "implementations.problem_classes.boussinesq_helpers.helper_classes.Callback.getcounter"]], "getresidual() (callback method)": [[136, "implementations.problem_classes.boussinesq_helpers.helper_classes.Callback.getresidual"]], "implementations.problem_classes.boussinesq_helpers.helper_classes": [[136, "module-implementations.problem_classes.boussinesq_helpers.helper_classes"]], "logging (class in implementations.problem_classes.boussinesq_helpers.helper_classes)": [[136, "implementations.problem_classes.boussinesq_helpers.helper_classes.logging"]], "numsmalltimesteps() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.NumSmallTimeSteps"]], "rk3lin() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.RK3Lin"]], "splitexplicit (class in implementations.problem_classes.boussinesq_helpers.standard_integrators)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit"]], "verletlin() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.VerletLin"]], "bdf2 (class in implementations.problem_classes.boussinesq_helpers.standard_integrators)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.bdf2"]], "dirk (class in implementations.problem_classes.boussinesq_helpers.standard_integrators)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.dirk"]], "f() (bdf2 method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.bdf2.f"]], "f() (trapezoidal method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.trapezoidal.f"]], "f_fast() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.f_fast"]], "f_fastmom() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.f_fastMom"]], "f_fastther() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.f_fastTher"]], "f_slow() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.f_slow"]], "f_solve() (bdf2 method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.bdf2.f_solve"]], "f_solve() (trapezoidal method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.trapezoidal.f_solve"]], "implementations.problem_classes.boussinesq_helpers.standard_integrators": [[137, "module-implementations.problem_classes.boussinesq_helpers.standard_integrators"]], "rk_imex (class in implementations.problem_classes.boussinesq_helpers.standard_integrators)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.rk_imex"]], "timestep() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.timestep"]], "trapezoidal (class in implementations.problem_classes.boussinesq_helpers.standard_integrators)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.trapezoidal"]], "implementations.problem_classes.boussinesq_helpers.unflatten": [[138, "module-implementations.problem_classes.boussinesq_helpers.unflatten"]], "unflatten() (in module implementations.problem_classes.boussinesq_helpers.unflatten)": [[138, "implementations.problem_classes.boussinesq_helpers.unflatten.unflatten"]], "a (genericndimfindiff attribute)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.A"]], "genericndimfindiff (class in implementations.problem_classes.generic_nd_fd)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff"]], "id (genericndimfindiff attribute)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.Id"]], "dtype_f (genericndimfindiff attribute)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.dtype_f"]], "dtype_u (genericndimfindiff attribute)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.dtype_u"]], "dx (genericndimfindiff property)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.dx"]], "eval_f() (genericndimfindiff method)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.eval_f"]], "get_default_sweeper_class() (genericndimfindiff class method)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.get_default_sweeper_class"]], "grids (genericndimfindiff property)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.grids"]], "implementations.problem_classes.generic_nd_fd": [[139, "module-implementations.problem_classes.generic_ND_FD"]], "ndim (genericndimfindiff property)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.ndim"]], "solve_system() (genericndimfindiff method)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.solve_system"]], "xvalues (genericndimfindiff attribute)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.xvalues"]], "dtype_f (nonlinear_ode_1 attribute)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.dtype_f"]], "dtype_u (nonlinear_ode_1 attribute)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.dtype_u"]], "eval_f() (nonlinear_ode_1 method)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.eval_f"]], "implementations.problem_classes.nonlinear_ode_1": [[140, "module-implementations.problem_classes.nonlinear_ODE_1"]], "newton_itercount (nonlinear_ode_1 attribute)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.newton_itercount"]], "newton_ncalls (nonlinear_ode_1 attribute)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.newton_ncalls"]], "nonlinear_ode_1 (class in implementations.problem_classes.nonlinear_ode_1)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1"]], "solve_system() (nonlinear_ode_1 method)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.solve_system"]], "u_exact() (nonlinear_ode_1 method)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.u_exact"]], "dtype_f (polynomial_testequation attribute)": [[141, "implementations.problem_classes.polynomial_test_problem.polynomial_testequation.dtype_f"]], "dtype_u (polynomial_testequation attribute)": [[141, "implementations.problem_classes.polynomial_test_problem.polynomial_testequation.dtype_u"]], "eval_f() (polynomial_testequation method)": [[141, "implementations.problem_classes.polynomial_test_problem.polynomial_testequation.eval_f"]], "implementations.problem_classes.polynomial_test_problem": [[141, "module-implementations.problem_classes.polynomial_test_problem"]], "polynomial_testequation (class in implementations.problem_classes.polynomial_test_problem)": [[141, "implementations.problem_classes.polynomial_test_problem.polynomial_testequation"]], "solve_system() (polynomial_testequation method)": [[141, "implementations.problem_classes.polynomial_test_problem.polynomial_testequation.solve_system"]], 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\ No newline at end of file
+Search.setIndex({"docnames": ["CHANGELOG", "CODE_OF_CONDUCT", "CONTRIBUTING", "README", "docs/contrib/01_pull_requests", "docs/contrib/02_continuous_integration", "docs/contrib/03_naming_conventions", "docs/contrib/04_custom_implementations", "docs/contrib/05_documenting_code", "index", "projects/AllenCahn_Bayreuth", "projects/DAE", "projects/Hamiltonian", "projects/PinTSimE", "projects/RDC", "projects/Resilience", "projects/SDC_showdown", "projects/asymp_conv", "projects/compression", "projects/doc_SDC_showdown", "projects/doc_asympconv", "projects/doc_fput", "projects/doc_fwsw_acoustic", "projects/doc_fwsw_boussinesq", "projects/doc_fwsw_theory", "projects/doc_hamiltonian_simple", "projects/doc_matrixPFASST_matrix", "projects/doc_matrixPFASST_propagator", "projects/doc_parallelSDC_nonlinear", "projects/doc_parallelSDC_preconditioner", "projects/doc_parallelSDC_preconditioner_MPI", "projects/doc_performance", "projects/doc_solar_system", "projects/fwsw", "projects/matrixPFASST", 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"&lt;no title&gt;", "&lt;no title&gt;", "&lt;no title&gt;", "&lt;no title&gt;", "Step-1: A first spatial problem", "Step-2: Data structures and my first sweeper", "Step-3: Statistics and a new sweeper", "Step-4: Multilevel SDC", "Step-5: PFASST", "Step-6: Advanced PFASST controllers", "Step-7: pySDC with external libraries", "Step-8: Advanced topics"], "terms": {"back": [0, 1, 2, 4, 5, 6, 7, 8, 165, 191], "main": [0, 1, 2, 5, 9, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 36, 39, 62, 63, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "page": [0, 1, 2, 9, 18, 53, 107, 109, 114, 120, 145], "juli": 0, "28": [0, 119], "2023": [0, 107, 109, 114, 139, 171, 173, 192, 193], "For": [0, 1, 3, 4, 6, 8, 9, 12, 15, 18, 26, 33, 34, 36, 42, 45, 62, 63, 65, 66, 88, 91, 92, 94, 95, 96, 97, 99, 102, 106, 107, 109, 120, 122, 139, 140, 144, 145, 146, 149, 150, 180, 186, 187, 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34, 35, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "merg": [0, 4, 41], "thank": 0, "brownbaerchen": 0, "tlunet": 0, "lisawim": 0, "ikrom96git": 0, "all": [0, 1, 3, 5, 6, 9, 10, 12, 14, 16, 17, 18, 19, 26, 27, 29, 30, 33, 34, 35, 40, 41, 42, 44, 45, 46, 51, 62, 63, 65, 66, 67, 69, 70, 73, 74, 78, 85, 90, 99, 105, 115, 122, 139, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 166, 168, 172, 179, 182, 184, 185, 191, 192, 193, 194, 195, 196, 197, 198], "contribut": [0, 1, 5, 6, 7, 8], "besid": 0, "usual": [0, 6, 18, 77, 195, 197], "bugfix": 0, "polish": 0, "pysdc": [0, 4, 7, 8, 10, 11, 12, 14, 16, 19, 21, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 44, 46, 48, 49, 50, 51, 56, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 94, 99, 119, 123, 125, 126, 141, 144, 156, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 193, 194, 195, 196, 198], "now": [0, 3, 9, 10, 13, 18, 34, 35, 42, 67, 144, 169, 176, 191, 192, 193, 194, 195, 196, 198], "come": [0, 4, 5, 10, 15, 18, 28, 35, 42, 191, 196, 198], "linear": [0, 7, 11, 16, 17, 19, 28, 34, 35, 73, 88, 89, 90, 91, 92, 94, 95, 96, 97, 99, 100, 101, 102, 107, 108, 109, 110, 112, 114, 115, 119, 120, 123, 124, 125, 127, 139, 141, 167, 168, 187, 191, 197], "multistep": [0, 142], "method": [0, 3, 6, 8, 9, 11, 12, 13, 14, 15, 33, 34, 35, 39, 41, 42, 44, 45, 48, 50, 63, 65, 66, 72, 73, 74, 77, 91, 92, 98, 99, 100, 108, 112, 113, 118, 119, 120, 124, 126, 127, 137, 139, 140, 143, 144, 145, 166, 168, 191, 197, 198], "classic": [0, 2, 3, 9, 12, 16, 19, 21, 25, 28, 32, 35, 144], "rung": [0, 66, 72, 144, 145], "kutta": [0, 66, 72, 144, 145], "dae": 0, "sweeper": [0, 3, 6, 9, 11, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 37, 38, 46, 65, 70, 72, 77, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 156, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198], "more": [0, 2, 3, 5, 7, 8, 9, 10, 12, 13, 16, 18, 19, 25, 32, 33, 35, 55, 66, 71, 72, 122, 169, 173, 174, 176, 177, 178, 185, 191, 192, 193, 194, 195, 197, 198], "improv": [0, 4, 6, 8, 13, 18, 193, 194], "project": [0, 3, 4, 5, 10, 12, 13, 14, 15, 16, 18, 19, 21, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 99, 108, 112, 113, 127, 157, 198], "we": [0, 1, 3, 5, 8, 9, 12, 13, 14, 15, 16, 17, 18, 25, 33, 34, 35, 36, 41, 42, 45, 53, 62, 65, 66, 67, 69, 70, 71, 72, 73, 74, 77, 78, 79, 99, 119, 124, 143, 144, 145, 169, 170, 171, 175, 176, 184, 185, 191, 192, 193, 194, 195, 196, 197, 198], "have": [0, 1, 4, 5, 6, 9, 12, 13, 15, 25, 27, 34, 35, 36, 42, 48, 65, 66, 67, 72, 73, 74, 77, 82, 83, 84, 86, 90, 92, 143, 144, 145, 169, 179, 185, 191, 192, 193, 194, 195, 196, 197, 198], "second": [0, 5, 9, 15, 21, 25, 32, 33, 34, 38, 47, 66, 73, 74, 82, 84, 91, 92, 104, 105, 106, 108, 110, 111, 114, 117, 119, 121, 144, 145, 146, 149, 150, 153, 154, 156, 190, 193, 198], "order": [0, 3, 5, 8, 9, 10, 11, 13, 15, 16, 18, 19, 21, 25, 26, 27, 29, 30, 32, 33, 34, 35, 36, 41, 42, 45, 47, 54, 58, 65, 66, 67, 69, 71, 72, 73, 74, 75, 80, 82, 84, 85, 88, 90, 91, 92, 100, 104, 106, 108, 111, 112, 113, 114, 115, 117, 122, 124, 127, 129, 130, 131, 133, 134, 135, 137, 139, 143, 144, 145, 146, 150, 152, 153, 154, 166, 168, 171, 173, 175, 181, 185, 190, 191, 192, 193, 194, 195, 197, 198], "sdc": [0, 2, 3, 9, 12, 13, 14, 18, 19, 28, 34, 50, 62, 63, 66, 68, 72, 73, 76, 78, 104, 124, 146, 150, 170, 171, 172, 173, 174, 177, 178, 181, 185, 186, 189, 190, 191, 192, 193, 195, 196, 197], "board": [0, 94, 95], "brand": 0, "new": [0, 3, 4, 5, 7, 8, 9, 11, 13, 34, 35, 50, 63, 65, 71, 77, 78, 79, 100, 107, 109, 143, 144, 145, 166, 168, 172, 184, 191, 196], "switch": [0, 65, 66, 72, 99, 101, 102], "estim": [0, 13, 15, 62, 66, 68, 71, 72, 74, 75, 76, 99, 102, 182, 190, 196], "test": [0, 2, 3, 4, 10, 11, 12, 13, 16, 17, 18, 19, 26, 27, 33, 34, 35, 36, 68, 79, 102, 108, 112, 113, 125, 127, 141, 145, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "ground": 0, "compress": [0, 9], "libpressio": [0, 18], "march": [0, 11, 73], "24": [0, 12, 32, 144, 180, 181, 195], "2": [0, 5, 6, 7, 9, 11, 12, 14, 16, 17, 19, 21, 26, 27, 28, 29, 30, 32, 33, 34, 35, 39, 44, 48, 58, 65, 66, 73, 82, 83, 84, 86, 88, 89, 90, 91, 92, 94, 95, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 119, 120, 121, 122, 123, 124, 126, 127, 139, 140, 144, 165, 166, 168, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 193, 194, 195, 196, 197, 198], "i": [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 21, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 41, 42, 44, 45, 47, 50, 55, 62, 63, 65, 66, 67, 68, 70, 72, 73, 74, 75, 77, 78, 79, 80, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 156, 164, 165, 166, 168, 169, 170, 171, 172, 173, 175, 176, 177, 179, 180, 181, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "out": [0, 3, 9, 11, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 62, 63, 72, 122, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "code": [0, 2, 3, 4, 6, 7, 9, 10, 12, 16, 18, 19, 21, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 70, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "multipl": [0, 13, 18, 41, 42, 44, 50, 65, 73, 74, 149, 176, 181, 185, 186, 192, 193, 194, 195, 196, 197], "direct": [0, 18, 66, 79, 90, 92, 96, 97, 100, 107, 109, 114, 115, 118, 124, 139, 164, 171, 192], "The": [0, 1, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 26, 27, 33, 34, 35, 36, 38, 39, 41, 42, 45, 47, 48, 51, 53, 54, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141, 143, 144, 146, 147, 148, 149, 150, 152, 153, 154, 156, 191, 192, 194, 195, 197, 198], "problem": [0, 2, 3, 6, 9, 11, 15, 16, 17, 18, 19, 21, 25, 26, 27, 28, 29, 30, 32, 33, 34, 37, 41, 43, 46, 49, 56, 65, 66, 70, 72, 73, 74, 76, 78, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 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97, 99, 100, 101, 104, 106, 107, 108, 110, 115, 123, 139, 144, 145, 146, 150, 157, 158, 159, 160, 161, 162, 163, 169, 180, 182, 185, 186, 187, 190, 191, 192, 193, 194, 195, 196, 197, 198], "defin": [0, 2, 3, 6, 7, 9, 34, 36, 38, 39, 48, 50, 66, 67, 68, 70, 76, 78, 79, 80, 101, 102, 103, 106, 107, 108, 111, 112, 113, 114, 127, 139, 146, 150, 171, 173, 181, 192, 193, 194, 195, 197], "paramet": [0, 4, 7, 8, 10, 11, 12, 14, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 84, 85, 86, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141, 143, 144, 145, 146, 149, 150, 151, 152, 156, 157, 159, 160, 161, 162, 163, 164, 166, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "explicitli": [0, 89, 91, 94, 95, 96, 97, 112, 113, 197], "constructor": [0, 7], "dictionari": [0, 12, 16, 19, 21, 25, 26, 27, 28, 32, 34, 35, 40, 42, 43, 44, 50, 57, 65, 66, 67, 68, 70, 74, 76, 78, 79, 80, 99, 149, 166, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "param": [0, 6, 29, 30, 35, 38, 40, 41, 42, 46, 49, 50, 51, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 166, 168, 170, 175, 191, 192, 194], "properti": [0, 8, 33, 40, 41, 45, 46, 48, 50, 51, 73, 82, 84, 139, 144, 149, 197], "return": [0, 7, 8, 12, 16, 19, 21, 25, 26, 27, 32, 34, 38, 39, 41, 42, 44, 45, 46, 47, 48, 50, 51, 53, 54, 55, 56, 57, 58, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 82, 84, 85, 86, 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144, 173, 174, 178, 180, 181, 182, 183, 184, 186, 187, 188, 189, 193, 194, 195, 196, 197, 198], "6th": 0, "workshop": 0, "avail": [0, 1, 5, 9, 14, 18, 36, 39, 42, 66, 72, 73, 143, 144], "index": [0, 5, 9, 11, 29, 30, 35, 65, 72, 73, 78, 99, 102], "http": [0, 1, 3, 5, 8, 9, 12, 21, 45, 75, 96, 97, 100, 104, 105, 107, 109, 110, 114, 120, 140, 144, 145], "org": [0, 1, 3, 5, 8, 9, 12, 21, 75, 98, 100, 104, 105, 107, 109, 110, 114, 119, 120, 144, 145], "simpli": [0, 5, 16, 192, 193, 194, 195, 198], "pip": [0, 3, 5, 9, 10], "natur": [0, 1, 11, 119, 193], "notabl": [0, 41, 66], "meet": 0, "standard": [0, 2, 11, 14, 16, 33, 34, 35, 38, 72, 73, 122, 156, 191, 193, 194, 195, 196], "2016": [0, 3, 9, 75, 88, 103, 150], "its": [0, 3, 5, 6, 9, 12, 53, 66, 73, 102, 124, 165, 166, 191, 192, 193, 194, 195], "redesign": 0, "core": [0, 3, 4, 5, 7, 9, 12, 149, 167, 168, 169, 170, 171, 173, 176, 191, 192, 193, 194, 197], "actual": [0, 13, 14, 44, 99, 122, 124, 144, 145, 170, 185, 191, 192, 193, 195, 196, 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104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 120, 124, 127, 139, 156, 158, 160, 162, 165, 166, 169, 175, 179, 180, 181, 187, 190, 192, 193, 195, 197, 198], "discret": [0, 8, 13, 18, 45, 54, 88, 89, 90, 91, 92, 99, 100, 102, 106, 107, 109, 110, 114, 115, 120, 124, 139, 165, 166, 190, 191, 197, 198], "formul": [0, 11, 34, 105, 108, 112, 113, 121, 127, 146, 147, 148, 149, 150, 152, 153, 154, 191], "move": [0, 66, 67, 193], "mlsdc": [0, 3, 9, 12, 34, 50, 62, 63, 177, 178, 185, 186, 195, 196, 197, 198], "inclus": [0, 1, 39], "two": [0, 10, 11, 12, 13, 16, 33, 34, 36, 39, 47, 50, 66, 68, 72, 74, 75, 88, 91, 92, 94, 95, 98, 100, 101, 103, 106, 108, 109, 110, 112, 113, 114, 124, 127, 139, 144, 145, 153, 166, 168, 178, 191, 194, 195, 196, 198], "gener": [0, 6, 7, 9, 11, 15, 17, 23, 33, 35, 39, 47, 48, 54, 56, 94, 95, 106, 107, 109, 120, 139, 143, 148, 149, 185, 193, 194, 197], "input": [0, 10, 13, 48, 56, 58, 107, 109, 148, 192], "nonmpi": [0, 42], "real": [0, 11, 35, 96, 97, 110, 118, 120, 159, 186, 191, 195, 197], "virtual": [0, 3, 9, 12, 63, 195], "parallelisim": 0, "simplifi": [0, 6, 8, 28], "coarsen": [0, 12, 14, 185, 194, 197, 198], "libpfasst": 0, "offer": [0, 192], "plugin": [0, 195, 198], "subpackag": 0, "fulli": [0, 3, 9, 11, 16, 19, 38, 42, 47, 66, 88, 89, 91, 92, 99, 103, 107, 109, 113, 120, 122, 124, 127, 191], "sphinx": [0, 5, 9], "apidoc": [0, 9], "mainli": [0, 9], "realiz": [0, 9, 26, 27, 34, 108, 109, 114, 196], "clearli": [0, 9], "stabl": [0, 144, 191], "barycentr": [0, 8, 45, 58], "interpol": [0, 8, 13, 38, 45, 58, 65, 66, 72, 74, 77, 99, 112, 113, 175, 178, 194, 195], "equidistantspline_right": 0, "spline": 0, "multi": [0, 3, 9, 15, 16, 19, 66, 91, 92, 107, 110, 153, 179, 182, 189, 191, 192, 195, 196], "aka": [0, 16], "singl": [0, 1, 5, 18, 26, 27, 34, 46, 57, 68, 122, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 169, 170, 171, 172, 173, 174, 178, 182, 185, 186, 192, 193, 194, 196, 197, 198], "level": [0, 1, 3, 6, 9, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 37, 38, 42, 43, 44, 49, 50, 51, 62, 63, 65, 66, 71, 72, 73, 78, 80, 143, 144, 149, 152, 156, 157, 158, 159, 160, 161, 162, 163, 164, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "expect": [0, 4, 9, 13, 28, 35, 73, 84, 148, 165, 166, 167, 168, 169, 172, 173, 174, 175, 177, 188, 190, 191, 192, 193, 194, 196, 197, 198], "rework": 0, "intern": [0, 13, 122, 192], "simplic": 0, "member": 1, "leader": 1, "particip": 1, "harass": 1, "free": [1, 26, 27, 34, 35, 65, 171, 173, 187, 192, 193, 197], "experi": [1, 9, 13, 15, 104, 166, 168, 191, 193], "everyon": 1, "regardless": 1, "ag": 1, "bodi": [1, 105, 121], "size": [1, 7, 8, 13, 15, 18, 38, 42, 45, 46, 50, 54, 62, 66, 67, 69, 73, 75, 77, 78, 79, 88, 100, 104, 107, 122, 139, 167, 168, 184, 190, 191, 196, 198], "disabl": [1, 9], "ethnic": 1, "sex": 1, "characterist": [1, 195], "gender": 1, "ident": [1, 48, 88, 90, 100, 109, 114, 115, 124, 139], "express": [1, 99, 101, 112, 113, 123], "educ": [1, 3, 9], "socio": 1, "econom": 1, "statu": [1, 37, 42, 46, 50, 62, 63, 65, 66, 67, 68, 71, 72, 107, 109, 170, 192], "nation": [1, 18], "person": [1, 4], "appear": [1, 11], "race": 1, "religion": 1, "sexual": 1, "orient": [1, 2], "interact": [1, 26, 27, 34, 122, 194], "open": [1, 5, 12, 13, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "welcom": [1, 171, 173, 192, 193], "divers": 1, "healthi": 1, "posit": [1, 12, 16, 19, 21, 25, 28, 32, 35, 85, 104, 105, 111, 117, 121, 122, 146, 154, 173, 178, 180, 181, 185, 186, 187, 193, 194, 195, 197], "demonstr": [1, 9, 10, 18, 187, 188, 192, 193, 194, 195, 196, 197, 198], "empathi": 1, "kind": [1, 39, 45, 92, 193, 195], "peopl": 1, "Being": 1, "respect": [1, 18, 26, 27, 33, 34], "opinion": 1, 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2, 3, 4, 7, 8, 9, 10, 12, 16, 18, 19, 21, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 40, 42, 43, 44, 45, 50, 56, 57, 65, 66, 77, 79, 90, 122, 139, 165, 166, 167, 168, 170, 171, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "clarifi": [1, 13], "take": [1, 3, 9, 10, 11, 18, 29, 30, 34, 35, 41, 47, 48, 67, 78, 90, 139, 166, 168, 185, 191, 194, 197, 198], "appropri": [1, 100, 141, 191], "fair": 1, "deem": 1, "threaten": 1, "offens": 1, "harm": 1, "edit": 1, "reject": 1, "commit": [1, 2, 4, 5, 15], "wiki": [1, 105, 145], "issu": [1, 3, 4, 5, 9, 144], "align": [1, 16, 19], "moder": 1, "appli": [1, 5, 11, 13, 18, 35, 38, 112, 144, 156], "offici": 1, "repres": [1, 7, 170, 191, 192, 195], "mail": 1, "post": [1, 5, 44, 192], "via": [1, 3, 9, 10, 17, 26, 27, 33, 34, 35, 38, 46, 49, 50, 66, 68, 94, 95, 112, 156, 157, 158, 159, 160, 161, 162, 195], "social": 1, "media": 1, "account": [1, 4, 47, 105, 121, 194], 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109, 110, 115, 120, 127, 139, 158, 159, 160, 161, 162, 181, 187, 190, 195, 197, 198], "channel": [1, 5], "term": [1, 10, 47, 73, 92, 94, 95, 104, 112, 113, 114, 115, 122, 124, 192], "lead": [1, 42, 124, 144, 145, 194, 198], "seriou": [1, 198], "sustain": 1, "pattern": 1, "aggress": [1, 14, 185, 197], "disparag": 1, "www": [1, 3, 9, 12, 21, 104, 105, 110, 140], "code_of_conduct": 1, "html": [1, 5, 105, 110, 120], "inspir": [1, 6, 8, 45, 47], "mozilla": 1, "ladder": 1, "answer": [1, 18], "common": [1, 11, 13, 37], "question": [1, 18, 198], "faq": 1, "translat": 1, "develop": [2, 3, 5, 6, 8, 9, 13, 95, 119], "approach": [2, 3, 5, 9, 34, 35, 139, 185, 195, 197], "fork": [2, 4, 5], "extend": [2, 122, 193], "skip": 2, "furthermor": 2, "branch": [2, 5, 15], "pre": [2, 4, 5, 29, 30, 35, 178, 192, 194], "To": [2, 3, 5, 9, 11, 139, 193, 194, 195, 196, 197], "pleas": [2, 3, 5, 9, 15, 44, 57, 66, 72, 79, 144, 145, 149, 192, 193], "addition": [2, 91], "rule": [2, 5, 6, 45, 47, 65, 66, 72, 143, 144, 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150, 152, 153, 180, 181, 186, 187, 190, 192, 195, 197, 198], "imex": [3, 9, 26, 33, 34, 88, 141, 144, 150, 152, 170, 171, 172, 173, 174, 178, 180, 186, 187, 190, 192, 193, 194, 195, 197, 198], "verlet": [3, 9, 12, 21, 25, 32, 142, 145, 146], "diagon": [3, 9, 26, 27, 34, 35, 125, 144], "topic": [3, 9, 18], "outcom": [3, 9, 18], "gitlab": [3, 9], "10": [3, 8, 9, 12, 14, 16, 19, 21, 25, 28, 29, 30, 32, 35, 75, 97, 98, 100, 101, 105, 107, 109, 114, 119, 124, 144, 145, 166, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 185, 186, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "host": [3, 4, 9], "com": [3, 9, 45, 145], "often": [3, 9, 18, 66], "choic": [3, 5, 9, 144, 145, 195], "thu": [3, 9, 11, 13, 191, 194], "checkout": [3, 9], "conda": [3, 5, 9, 10], "found": [3, 9, 12, 13, 14, 29, 30, 33, 35, 42, 58, 99, 102, 193, 197], "folder": [3, 5, 9, 10, 197], "etc": [3, 5, 9, 36, 42, 66, 69, 73, 75, 194, 195], "env": [3, 9, 184, 196], "creat": [3, 9, 10, 12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 44, 99, 108, 112, 113, 127, 139, 165, 166, 167, 168, 169, 176, 187, 188, 191, 192, 193, 194, 195, 197, 198], "yml": [3, 9], "m": [3, 5, 8, 9, 11, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 42, 45, 63, 67, 73, 74, 75, 78, 100, 108, 112, 113, 122, 124, 127, 131, 167, 168, 171, 172, 173, 174, 177, 178, 179, 180, 181, 182, 185, 186, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "correspond": [3, 5, 9, 12, 18, 25, 26, 27, 33, 34, 42, 47, 50, 57, 65, 146, 147, 148, 149, 150, 151, 152, 153, 154, 194, 196, 198], "chose": [3, 9, 119], "pythonpath": [3, 9, 184, 196], "export": [3, 5, 9], "path": [3, 5, 9, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 42, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "root": [3, 5, 9, 11, 13, 82, 84, 86, 102, 184, 196], "want": [3, 5, 9, 18, 42, 65, 66, 67, 70, 72, 73, 78, 145, 192, 196, 198], 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97, 99, 100, 101, 103, 105, 106, 107, 109, 114, 121, 122, 123, 124, 139, 156, 198], "messag": [5, 42, 62, 65, 66, 69, 73, 74, 75], "detect": [5, 18, 75], "abort": [5, 26, 27, 34, 70], "ahead": 5, "worri": [5, 196], "obtain": [5, 8, 34, 35, 45, 54, 65, 66, 72, 73, 108], "msg": [5, 42, 70], "commit_msg_fil": 5, "flakeheaven_output": 5, "interpret": 5, "trailer": 5, "echo": 5, "assign": [5, 29, 30, 35, 141], "note": [5, 6, 8, 12, 14, 16, 17, 19, 26, 27, 33, 34, 45, 72, 171, 185, 186, 191, 192, 193, 194, 195, 196, 197, 198], "relat": [5, 33, 38, 42, 48, 49, 50, 51, 156, 193], "constantli": [5, 124], "pep8": [5, 9], "might": [5, 18, 55, 77, 79, 196], "caus": [5, 15, 144, 196], "date": 5, "forg": 5, "pass": [5, 6, 8, 16, 19, 26, 27, 29, 30, 34, 35, 38, 42, 46, 48, 50, 51, 53, 57, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 78, 79, 80, 156, 179, 180, 181, 186, 187, 190, 191, 192, 194, 195, 197, 198], "toml": [5, 184, 196], "compon": [5, 10, 11, 13, 82, 83, 84, 86, 98, 110, 118, 119, 126, 140, 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43, 44, 62, 73, 82, 84, 86, 108, 109, 110, 171, 173, 179, 180, 181, 182, 183, 184, 188, 189, 192, 193, 195, 196, 198], "combin": [5, 11, 12, 73, 184, 187, 194, 196, 197], "htmlcov": 5, "favorit": [5, 144], "browser": 5, "did": [5, 12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 73, 166, 167, 168, 169, 170, 171, 175, 184, 187, 191, 192, 194, 196, 197], "ignor": [5, 144, 145, 198], "rais": [5, 6, 7, 12, 16, 19, 25, 26, 27, 32, 34, 42, 70, 184, 185, 196, 197], "tool": [5, 36, 192], "pyproject": [5, 184, 196], "conditionali": 5, "loop": [5, 13, 16, 19, 28, 29, 30, 35, 44, 166, 168, 174, 180, 181, 182, 191, 193, 195, 196], "pragma": 5, "cover": 5, "def": [5, 6, 7, 8, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "preced": 5, "think": 5, "justifi": 5, "built": [5, 6, 144, 145, 192, 198], "task": [5, 196], "doc": [5, 120], "unzip": 5, "rst": 5, "update_apidoc": 5, "b": [5, 16, 19, 26, 27, 28, 29, 30, 34, 35, 65, 73, 74, 100, 108, 109, 110, 112, 113, 122, 127, 131, 137, 173, 178, 179, 180, 181, 187, 190], "Then": [5, 8, 13, 14, 45, 191, 193], "graph": [5, 28, 35], "imag": 5, "still": [5, 35, 42, 65, 74, 141, 144], "miss": [5, 198], "concern": 5, "mostli": [6, 43], "Of": [6, 194], "cours": [6, 42, 194], "strictli": [6, 144, 145], "alwai": [6, 15, 44, 66, 78, 101, 144, 145, 146, 154, 191, 194, 196], "guido": 6, "von": 6, "rossum": 6, "kei": [6, 12, 16, 19, 21, 25, 29, 30, 32, 35, 55, 57, 62, 63, 73, 99, 139, 174, 184, 192, 193, 195, 196], "insight": 6, "state": [6, 13, 35, 96, 97, 99, 101, 102], "foolish": 6, "hobgoblin": 6, "littl": [6, 186, 191, 193, 197], "mind": [6, 48, 54, 74, 141], "find": [6, 9, 13, 15, 18, 29, 30, 35, 42, 58, 166, 168, 191], "optim": [6, 11, 35, 66, 120, 166, 168, 191], "compromis": 6, "someon": [6, 9], "els": [6, 12, 16, 19, 25, 26, 27, 29, 30, 32, 34, 35, 66, 99, 102, 149, 178, 182, 184, 185, 186, 187, 190, 194, 196, 197, 198], "understand": [6, 8, 36], "my": [6, 9], "effect": [6, 66, 119, 124], "kilomet": 6, "aspect": [6, 18], "interdepend": 6, "attract": 6, "lowercas": 6, "variablenamelikethi": 6, "snake_cas": 6, "variable_name_like_thi": 6, "pascalcas": 6, "camelcas": 6, "uppercas": 6, "minu": 6, "try": [6, 14, 15, 65, 66, 72, 184, 191, 196], "stick": 6, "discourag": 6, "advectiondiffus": 6, "except": [6, 15, 42, 43, 47, 124, 184, 196], "suffix": [6, 195], "parametererror": [6, 37, 43], "goe": [6, 42], "argument": [6, 42, 44, 48, 57, 90, 172, 193], "tleft": [6, 39, 167, 168, 191], "quadtyp": 6, "legendr": [6, 39, 45, 47, 167, 168, 177, 191, 193, 194], "computefejerrul": [6, 37, 45], "nnode": [6, 176, 194], "nodegener": 6, "getorthogpolycoeff": 6, "self": [6, 7, 8, 42, 63, 68, 73, 99, 149], "ncoeff": 6, "abbrevi": 6, "deterior": [6, 13], "rather": [6, 8, 12, 13, 18, 33, 185, 192, 196, 197], "getorthogonalpolynomialcoeffici": 6, "plural": 6, "acronym": 6, 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194, 195, 196, 197, 198], "gauss": [6, 15, 18, 35, 39, 45, 47, 66, 72, 174, 193, 195, 198], "radau": [6, 16, 19, 26, 27, 28, 29, 30, 34, 35, 39, 167, 168, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "lobatto": [6, 12, 21, 25, 32, 39, 47, 174, 193], "string": [6, 16, 19, 41, 42, 46, 57, 139], "distinguish": 6, "select": [6, 66, 74], "probabl": [6, 122, 197], "keep": [6, 10, 41, 42, 48, 54, 74, 141, 182, 196], "replac": [6, 14, 16, 19, 193, 194], "_initsweep_copy_past": 6, "_initsweep_spread_out": 6, "non": [7, 17, 35, 42, 58, 62, 66, 67, 69, 73, 78, 82, 84, 85, 86, 119, 124, 196], "od": [7, 9, 48, 51, 98, 99, 101, 119, 123, 140, 143, 149, 194, 197], "form": [7, 9, 11, 90, 92, 94, 95, 96, 97, 108, 109, 110, 113, 115, 118, 125, 146, 150, 185, 191, 195, 197], "frac": [7, 8, 45, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 139, 140], "du": [7, 16, 19, 108, 109, 110, 118, 140], "dt": [7, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 45, 46, 50, 66, 73, 98, 99, 101, 102, 103, 111, 117, 118, 119, 122, 123, 125, 126, 131, 137, 139, 140, 167, 168, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "quad": 7, "u_0": [7, 11, 103], "vector": [7, 8, 11, 45, 54, 58, 65, 73, 74, 104, 105, 107, 108, 109, 112, 113, 121, 127, 158, 162, 167, 168, 191, 192], "scalar": [7, 8, 33, 45, 103, 108, 112, 113, 127, 146, 150], "hand": [7, 18, 42, 48, 51, 54, 65, 73, 77, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 154, 167, 168, 191, 192, 194, 197], "side": [7, 18, 48, 51, 54, 65, 77, 88, 89, 91, 92, 94, 95, 96, 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181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "super": [7, 42, 44, 110, 193], "init": [7, 8, 42, 48, 82, 83, 84, 85, 86, 165, 166, 175, 181, 191, 194, 195], "none": [7, 10, 12, 16, 19, 25, 26, 27, 28, 29, 30, 32, 34, 35, 39, 41, 42, 44, 46, 48, 54, 55, 57, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 82, 83, 84, 85, 86, 88, 92, 94, 95, 96, 97, 99, 100, 102, 104, 107, 108, 109, 110, 114, 119, 120, 123, 124, 125, 126, 127, 139, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 166, 168, 171, 173, 182, 185, 186, 190, 191, 192, 193, 196, 197, 198], "dtype": [7, 84, 173, 174, 178, 193, 194], "regist": [7, 40, 57, 172, 193], "localvar": 7, "true": [7, 12, 16, 19, 26, 27, 32, 34, 42, 46, 53, 58, 73, 91, 99, 102, 106, 110, 118, 119, 120, 124, 126, 139, 140, 144, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "rh": [7, 10, 38, 46, 48, 51, 73, 82, 83, 84, 86, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 106, 107, 108, 109, 110, 112, 113, 114, 118, 119, 120, 122, 123, 124, 125, 126, 127, 131, 137, 139, 140, 141, 143, 149, 156], "eval_f": [7, 48, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 139, 140, 141, 165, 166, 191], "f_init": [7, 48], "list": [7, 8, 9, 10, 12, 16, 19, 21, 25, 26, 27, 29, 30, 32, 34, 35, 41, 42, 45, 46, 48, 50, 53, 54, 57, 58, 63, 65, 67, 73, 74, 75, 78, 91, 94, 95, 96, 97, 99, 100, 102, 104, 108, 125, 127, 143, 144, 146, 147, 148, 149, 150, 151, 153, 154, 166, 168, 172, 173, 174, 175, 178, 180, 181, 182, 184, 189, 191, 193, 194, 195, 196, 198], "output": [7, 12, 13, 25, 32, 36, 44, 48, 65, 107, 109, 159, 173, 174, 178, 182, 184, 187, 193, 194, 196, 197], "fals": [7, 12, 16, 19, 32, 41, 42, 44, 53, 54, 58, 62, 63, 67, 72, 105, 118, 120, 121, 139, 147, 148, 149, 150, 151, 152, 153, 171, 173, 178, 182, 185, 186, 187, 189, 190, 192, 193, 194, 196, 197, 198], "docstr": 8, "itself": [8, 13, 42, 73, 124, 194, 198], "describ": [8, 9, 11, 16, 17, 19, 36, 99, 105, 108, 109, 110, 121, 172, 193], "lagrangeapproxim": [8, 37, 45], "approxim": [8, 11, 18, 45, 73, 74, 89, 91, 94, 95, 96, 97, 110, 118, 119, 120, 123, 124, 126], "point": [8, 13, 18, 39, 45, 46, 47, 53, 58, 65, 72, 73, 74, 89, 91, 92, 94, 95, 96, 97, 99, 102, 105, 107, 121, 124, 146, 147, 148, 149, 150, 151, 152, 153, 154, 165, 166, 191], "lagrang": [8, 37, 108, 112, 113, 127, 194], "math": [8, 100, 107], "t_j": [8, 45], "leq": [8, 45, 99, 101, 102, 115, 140], "j": [8, 45, 88, 92, 94, 95, 96, 97, 101, 103, 104, 105, 107, 108, 109, 112, 113, 121, 127, 144], "n": [8, 12, 16, 19, 21, 26, 27, 28, 32, 34, 35, 45, 90, 92, 94, 95, 96, 97, 99, 100, 104, 105, 106, 108, 110, 112, 113, 115, 120, 121, 122, 127, 129, 130, 133, 134, 135, 137, 139, 166, 167, 168, 170, 172, 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25, 28, 29, 30, 32, 35, 45, 53, 91, 92, 94, 95, 96, 97, 122, 191, 197], "getinterpolationmatrix": [8, 45], "vec": [8, 16, 19, 45, 86, 88, 91, 92, 99, 100, 101, 102, 103, 107, 108, 109, 112, 113, 114, 120, 123, 124, 125, 127, 139], "tau_m": [8, 45], "p_": [8, 45], "inter": [8, 45, 122], "pinter": [8, 45], "2darrai": [8, 45, 101, 122, 123], "row": [8, 45, 65, 67, 73, 74, 107, 150], "column": [8, 45, 73, 107, 150, 167, 168, 191], "cute": 8, "pictur": [8, 12, 18, 21, 36], "cat": 8, "coverag": 9, "flatten": [9, 48], "steep": 9, "curv": 9, "eight": 9, "briefli": [9, 198], "discuss": [9, 196], "along": [9, 13, 122], "highlight": 9, "shown": [9, 12, 16], "ye": [9, 54], "jupyt": [9, 15], "notebook": [9, 15], "awesom": [9, 39], "statist": [9, 12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 44, 57, 59, 62, 63, 91, 172, 173, 174, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 194, 195, 196, 197, 198], "gather": [9, 16, 44, 122, 166, 168, 174, 175, 184, 191, 193, 194, 196, 198], 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177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 193, 194, 195, 196, 197, 198], "tabl": [9, 39, 41], "search": 9, "materi": 10, "scienc": [10, 198], "paraphas": 10, "partner": 10, "flexibl": 10, "run_simple_forcing_verif": 10, "2d": [10, 11, 16, 33, 65, 74, 90, 92, 100, 114, 115, 160, 186, 197], "against": [10, 34], "known": [10, 11, 13, 42, 94, 95, 119, 122], "circl": [10, 91, 92, 94, 95, 96, 97], "shrink": [10, 167, 168, 191], "drive": [10, 91, 96, 97, 198], "vanish": [10, 73], "numer": [10, 11, 12, 18, 33, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 123, 124, 125, 126, 127, 140, 141, 145], "scheme": [10, 11, 33, 34, 35, 65, 66, 73, 74, 100, 143, 144, 145, 146, 195, 198], "constant": [10, 73, 92, 94, 95, 105, 111, 121, 122, 146, 195, 198], "dw": [10, 91, 96, 97], "radiu": [10, 17, 33, 35, 91, 92, 94, 95, 96, 97], "stai": [10, 101], "run_temp_forcing_verif": 10, "temperatur": [10, 119, 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171, 172, 173, 185, 188, 189, 192, 193, 194, 197], "fully_implicit_dae_playground": 11, "arena": 11, "synchronous_machine_playground": 11, "fully_implicit_da": 11, "represent": 11, "aris": [11, 13, 44, 91, 106, 118, 126, 139, 140], "jacobian": [11, 35, 47, 48, 107, 109, 124], "partial_": 11, "singular": [11, 140], "impli": [11, 197], "deriv": [11, 14, 34, 41, 44, 47, 54, 73, 88, 91, 100, 111, 124, 139, 140, 141, 150], "denot": [11, 72, 89, 91, 94, 95, 96, 97, 99, 103, 110, 111, 112, 113, 115, 120, 127], "isol": 11, "picard": [11, 146, 147, 148, 149, 150, 152, 153, 154], "ordinari": [11, 13, 15, 75, 98, 99, 101, 102, 119, 123], "henceforth": 11, "cast": 11, "unknown": [11, 73, 91, 92, 94, 95, 96, 97, 100, 111, 113], "int_0": 11, "tu": 11, "tau": [11, 38, 46, 156, 185, 197], "d": [11, 14, 28, 29, 35, 88, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 109, 110, 111, 112, 113, 114, 117, 119, 121, 123, 125, 126, 139, 184, 196], "tild": 11, "delta": [11, 29, 30, 35, 45, 91, 92, 94, 95, 96, 97, 103, 106, 107, 108, 109, 110, 120, 127], "t_": [11, 101, 119, 122], "t_m": [11, 97], "int_": [11, 45, 108, 112, 113, 127], "discretis": [11, 124, 139], "obviou": [11, 14], "mathbf": 11, "q": [11, 29, 30, 35, 51, 108, 122, 144, 145, 146, 149, 150, 152, 167, 168, 191], "l": [11, 28, 29, 30, 35, 58, 72, 89, 94, 95, 96, 97, 99, 110, 120, 144, 166, 168, 169, 170, 176, 191, 192, 194], "_l": 11, "low": 11, "euler": [11, 35, 100, 143, 144, 146, 147, 150, 152, 154, 181, 195], "_0": 11, "begin": [11, 42, 122, 171, 173, 192, 193, 196], "pmatrix": 11, "t_1": 11, "dot": [11, 27, 34], "t_2": 11, "clear": [11, 193], "repeatedli": 11, "recalcul": [11, 13], "reformul": [11, 112, 113, 127], "carri": [11, 42], "u_": [11, 104], "familiar": 11, "scipi": [11, 14, 45, 48, 88, 91, 92, 94, 95, 119, 120, 123, 124, 125, 126, 167, 168, 191], "3rd": 12, "harmon": [12, 25, 111], "oscil": [12, 14, 25, 111, 126], "henon": [12, 25], "heil": [12, 25, 117], "hamiltonian_output": [12, 25, 32], "monitor": [12, 13, 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16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 46, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "restol": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "1e": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 90, 91, 92, 98, 99, 100, 102, 106, 107, 109, 110, 114, 115, 118, 119, 120, 124, 126, 139, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "sweeper_param": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 46, 65, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "num_nod": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 39, 47, 65, 144, 145, 167, 168, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "initial_guess": [12, 16, 19, 21, 25, 26, 27, 32, 34, 144, 145, 171, 173, 186, 187, 190, 192, 193, 197, 198], "zero": [12, 16, 19, 21, 25, 26, 27, 29, 30, 32, 34, 35, 48, 73, 99, 101, 124, 165, 166, 167, 168, 169, 170, 171, 172, 175, 176, 177, 179, 180, 182, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "problem_param": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 46, 166, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "amp": [12, 25, 111], "step_param": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "maxit": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 76, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "50": [12, 16, 19, 21, 25, 26, 27, 28, 32, 34, 35, 127, 172, 178, 180, 181, 182, 183, 184, 186, 187, 188, 189, 190, 193, 194, 195, 196, 197, 198], "hook_class": [12, 21, 25, 28, 32, 35, 171, 173, 174, 178, 190, 192, 193, 194, 198], "logger_level": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 65, 171, 172, 173, 174, 177, 178, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "fill": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 51, 122, 143, 144, 149, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "easi": [12, 16, 19, 21, 25, 26, 27, 28, 32, 34, 35, 169, 170, 171, 172, 173, 174, 176, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 192, 193, 194, 195, 196, 197, 198], "hierarchi": [12, 21, 25, 28, 32, 35, 62, 63, 149, 170, 171, 172, 173, 174, 176, 178, 179, 185, 192, 193, 197], "space_transfer_class": [12, 16, 19, 21, 25, 26, 27, 32, 34, 38, 50, 156, 176, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198], "setup_henonheil": [12, 25], "run_simul": [12, 21, 25, 32, 172, 174, 186, 190, 193, 197, 198], "prob": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 46, 107, 109, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 176, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "arg": [12, 16, 19, 21, 25, 26, 27, 28, 32, 34, 35, 48, 70, 90, 165, 166, 167, 168, 170, 182, 184, 185, 186, 191, 192, 196, 197], "str": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 40, 41, 42, 45, 47, 51, 53, 54, 55, 57, 59, 65, 66, 69, 72, 73, 74, 75, 90, 94, 95, 96, 97, 108, 112, 113, 115, 124, 127, 139, 143, 149, 152, 175, 184, 185, 187, 194, 196, 197], "t0": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 41, 62, 63, 108, 112, 113, 167, 168, 171, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "tend": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 41, 42, 62, 63, 67, 73, 78, 79, 167, 168, 171, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "num_proc": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 62, 63, 171, 172, 173, 174, 177, 178, 179, 180, 181, 182, 184, 185, 186, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "maxmeanit": [12, 25, 32], "elif": [12, 16, 19, 25, 26, 27, 28, 29, 30, 32, 34, 35, 185, 190, 197, 198], "instanti": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 41, 42, 48, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 165, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "finest": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 50, 62, 63, 66, 72, 73, 78, 171, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "uinit": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 171, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "u_exact": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 140, 141, 166, 167, 168, 170, 171, 172, 173, 177, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "uend": [12, 16, 19, 21, 25, 28, 29, 30, 32, 34, 35, 46, 146, 147, 148, 149, 150, 152, 153, 154, 167, 168, 170, 171, 172, 173, 174, 178, 180, 181, 182, 184, 185, 186, 187, 188, 190, 191, 192, 193, 194, 195, 196, 197, 198], "stat": [12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 41, 44, 57, 59, 62, 63, 171, 172, 173, 174, 178, 180, 181, 182, 184, 185, 186, 187, 188, 190, 192, 193, 194, 195, 196, 197, 198], "u0": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 41, 50, 62, 63, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 106, 107, 108, 109, 110, 111, 112, 113, 114, 118, 119, 120, 122, 123, 124, 125, 126, 127, 131, 137, 139, 140, 141, 167, 168, 171, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198], "filter": [12, 16, 19, 21, 25, 27, 28, 29, 30, 32, 34, 35, 57, 172, 173, 174, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 193, 195, 196, 197, 198], "iter_count": [12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 172, 180, 181, 182, 184, 185, 186, 187, 188, 190, 193, 195, 196, 197, 198], "niter": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 48, 170, 172, 177, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "sortbi": [12, 16, 19, 21, 25, 26, 27, 28, 29, 30, 32, 34, 35, 57, 172, 173, 174, 177, 178, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 193, 194, 195, 196, 197, 198], "item": [12, 16, 19, 21, 25, 27, 28, 32, 34, 35, 57, 172, 173, 174, 178, 180, 181, 182, 184, 185, 186, 187, 188, 190, 193, 194, 195, 196, 197, 198], "2f": [12, 16, 19, 21, 25, 28, 32, 35, 170, 172, 175, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 198], "2i": [12, 16, 19, 21, 25, 28, 32, 35, 166, 168, 170, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 189, 191, 192, 193, 194, 195, 196, 197, 198], "mean": [12, 13, 14, 15, 16, 18, 19, 21, 25, 28, 32, 35, 72, 73, 79, 99, 101, 114, 124, 149, 180, 181, 185, 186, 187, 190, 195, 197, 198], "rang": [12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 99, 107, 124, 165, 166, 168, 175, 176, 179, 180, 181, 185, 186, 187, 190, 191, 194, 195, 197, 198], "ptp": [12, 16, 19, 21, 25, 28, 32, 35, 180, 181, 185, 186, 187, 195, 197], "max": [12, 16, 19, 21, 25, 28, 32, 35, 68, 90, 115, 166, 168, 180, 181, 185, 186, 187, 188, 191, 195, 197, 198], "min": [12, 16, 19, 21, 25, 28, 29, 30, 32, 35, 166, 168, 176, 180, 181, 185, 186, 187, 188, 191, 194, 195, 197, 198], "int": [12, 16, 19, 21, 25, 28, 32, 35, 39, 42, 44, 45, 46, 47, 54, 58, 62, 66, 67, 73, 78, 82, 84, 85, 86, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 118, 119, 122, 124, 126, 127, 139, 140, 146, 149, 150, 175, 180, 181, 185, 186, 187, 194, 195, 197], "argmax": [12, 16, 19, 21, 25, 28, 32, 35, 180, 181, 185, 186, 187, 195, 197], "argmin": [12, 16, 19, 21, 25, 28, 32, 35, 180, 181, 185, 186, 187, 195, 197], "std": [12, 16, 19, 21, 25, 28, 32, 35, 180, 181, 185, 186, 187, 195, 197], "var": [12, 16, 19, 21, 25, 28, 32, 35, 180, 181, 185, 186, 187, 195, 197], "float": [12, 16, 19, 21, 25, 26, 27, 28, 32, 34, 35, 39, 41, 42, 46, 47, 48, 50, 53, 54, 66, 67, 70, 73, 78, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 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Correction": [[1, "correction"]], "2. Warning": [[1, "warning"]], "3. Temporary Ban": [[1, "temporary-ban"]], "4. Permanent Ban": [[1, "permanent-ban"]], "Attribution": [[1, "attribution"]], "How to contribute to pySDC": [[2, "how-to-contribute-to-pysdc"]], "Welcome to pySDC!": [[3, "welcome-to-pysdc"], [9, "welcome-to-pysdc"]], "Features": [[3, "features"], [9, "features"]], "Getting started": [[3, "getting-started"], [9, "getting-started"]], "How to cite": [[3, "how-to-cite"], [9, "how-to-cite"]], "Contributing": [[3, "contributing"], [9, "contributing"]], "Acknowledgements": [[3, "acknowledgements"], [9, "acknowledgements"]], "Recommendations for pull requests": [[4, "recommendations-for-pull-requests"]], "Contributing to the main branch": [[4, "contributing-to-the-main-branch"]], "Release development branches": [[4, "release-development-branches"]], "Feature development branches": [[4, "feature-development-branches"]], "Continuous Integration in pySDC": [[5, "continuous-integration-in-pysdc"]], "Code linting": [[5, "code-linting"]], "Code testing": [[5, "code-testing"]], "Code coverage": [[5, "code-coverage"]], "Coverage exceptions": [[5, "coverage-exceptions"]], "Documentation generation": [[5, "documentation-generation"]], "Naming conventions in pySDC": [[6, "naming-conventions-in-pysdc"]], "First definitions": [[6, "first-definitions"]], "Packages and modules names": [[6, "packages-and-modules-names"]], "Class names": [[6, "class-names"]], "Function and variables names": [[6, "function-and-variables-names"]], "Private and public attributes": [[6, "private-and-public-attributes"]], "Constants": [[6, "constants"]], "Custom implementation guidelines": [[7, "custom-implementation-guidelines"]], "Implementing a custom problem class": [[7, "implementing-a-custom-problem-class"]], "Documenting Code": [[8, "documenting-code"]], "Tests": [[9, "tests"], [15, "tests"]], "User Guide": [[9, "user-guide"]], "Tutorial": [[9, "tutorial"]], "Playgrounds": [[9, "playgrounds"]], "Projects": [[9, "projects"]], "API documentation": [[9, "api-documentation"]], "Allen-Cahn problems from Bayreuth": [[10, "allen-cahn-problems-from-bayreuth"]], "Verification": [[10, "verification"]], "Benchmark": [[10, "benchmark"]], "Application": [[10, "application"]], "Further/related files": [[10, "further-related-files"]], "Solving differential algebraic equations with SDC": [[11, "solving-differential-algebraic-equations-with-sdc"]], "Project overview": [[11, "project-overview"]], "Theoretical details": [[11, "theoretical-details"]], "Second-order Problems": [[12, "second-order-problems"]], "Simple problems": [[12, "simple-problems"]], "Solar system problem": [[12, "solar-system-problem"]], "Fermi-Pasta-Ulam-Tsingou problem": [[12, "fermi-pasta-ulam-tsingou-problem"]], "Parallel-in-time simulation for multi-modal energy systems": [[13, "parallel-in-time-simulation-for-multi-modal-energy-systems"]], "What are switching processes in power systems?": [[13, "what-are-switching-processes-in-power-systems"]], "Pi-line": [[13, "pi-line"]], "Buck converter": [[13, "buck-converter"]], "Battery drain model": [[13, "battery-drain-model"]], "RDC: Rational Deferred Corrections": [[14, "rdc-rational-deferred-corrections"]], "Testing RDC convergence": [[14, "testing-rdc-convergence"]], "Multi-level RDC and PFASST with RDC": [[14, "multi-level-rdc-and-pfasst-with-rdc"]], "Resilience in SDC": [[15, "resilience-in-sdc"]], "What is the fastest SDC variant?": [[16, "what-is-the-fastest-sdc-variant"]], "Fisher and Gray-Scott equations": [[16, "fisher-and-gray-scott-equations"]], "Asymptotic convergence of PFASST": [[17, "asymptotic-convergence-of-pfasst"]], "Organisation of the project": [[17, "organisation-of-the-project"]], "Compression in pySDC": [[18, "compression-in-pysdc"]], "Introduction": [[18, "introduction"]], "Methods": [[18, "methods"]], "Proof of Concept": [[18, "proof-of-concept"]], "Fast-Wave-Slow-Wave SDC": [[33, "fast-wave-slow-wave-sdc"]], "Theoretical results": [[33, "theoretical-results"]], "Acoustic-advection example": [[33, "acoustic-advection-example"]], 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"implementations.problem_classes.acoustic_helpers.buildWave1DMatrix module": [[130, "module-implementations.problem_classes.acoustic_helpers.buildWave1DMatrix"]], "implementations.problem_classes.acoustic_helpers.standard_integrators module": [[131, "module-implementations.problem_classes.acoustic_helpers.standard_integrators"]], "implementations.problem_classes.boussinesq_helpers package": [[132, "implementations-problem-classes-boussinesq-helpers-package"]], "implementations.problem_classes.boussinesq_helpers.build2DFDMatrix module": [[133, "module-implementations.problem_classes.boussinesq_helpers.build2DFDMatrix"]], "implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix module": [[134, "module-implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix"]], "implementations.problem_classes.boussinesq_helpers.buildFDMatrix module": [[135, "module-implementations.problem_classes.boussinesq_helpers.buildFDMatrix"]], 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check": [[191, "part-b-spatial-accuracy-check"]], "Part C: Collocation problem setup": [[191, "part-c-collocation-problem-setup"]], "Part D: Collocation accuracy test": [[191, "part-d-collocation-accuracy-test"]], "Step-2: Data structures and my first sweeper": [[192, "step-2-data-structures-and-my-first-sweeper"]], "Part A: Step data structure": [[192, "part-a-step-data-structure"]], "Part B: My first sweeper": [[192, "part-b-my-first-sweeper"]], "Part C: Using pySDC\u2019s frontend": [[192, "part-c-using-pysdc-s-frontend"]], "Step-3: Statistics and a new sweeper": [[193, "step-3-statistics-and-a-new-sweeper"]], "Part A: Getting statistics": [[193, "part-a-getting-statistics"]], "Part B: Adding statistics": [[193, "part-b-adding-statistics"]], "Part C: Studying collocation node types": [[193, "part-c-studying-collocation-node-types"]], "Step-4: Multilevel SDC": [[194, "step-4-multilevel-sdc"]], "Part A: Spatial transfer operators": [[194, "part-a-spatial-transfer-operators"]], "Part 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"core.ConvergenceController.ConvergenceController.prepare_next_block"]], "reset_buffers_nonmpi() (convergencecontroller method)": [[42, "core.ConvergenceController.ConvergenceController.reset_buffers_nonMPI"]], "reset_status_variables() (convergencecontroller method)": [[42, "core.ConvergenceController.ConvergenceController.reset_status_variables"]], "reset_variable() (convergencecontroller method)": [[42, "core.ConvergenceController.ConvergenceController.reset_variable"]], "setup() (convergencecontroller method)": [[42, "core.ConvergenceController.ConvergenceController.setup"]], "setup_status_variables() (convergencecontroller method)": [[42, "core.ConvergenceController.ConvergenceController.setup_status_variables"]], "collocationerror": [[43, "core.Errors.CollocationError"]], "communicationerror": [[43, "core.Errors.CommunicationError"]], "controllererror": [[43, "core.Errors.ControllerError"]], "convergenceerror": [[43, "core.Errors.ConvergenceError"]], "dataerror": [[43, "core.Errors.DataError"]], "parametererror": [[43, "core.Errors.ParameterError"]], "problemerror": [[43, "core.Errors.ProblemError"]], "readonlyerror": [[43, "core.Errors.ReadOnlyError"]], "transfererror": [[43, "core.Errors.TransferError"]], "unlockerror": [[43, "core.Errors.UnlockError"]], "core.errors": [[43, "module-core.Errors"]], "entry (class in core.hooks)": [[44, "core.Hooks.Entry"]], "__num_restarts (hooks attribute)": [[44, "core.Hooks.hooks.__num_restarts"]], "__stats (hooks attribute)": [[44, "core.Hooks.hooks.__stats"]], "add_to_stats() (hooks method)": [[44, "core.Hooks.hooks.add_to_stats"]], "core.hooks": [[44, "module-core.Hooks"]], "entry (hooks attribute)": [[44, "core.Hooks.hooks.entry"], [44, "id0"]], "hooks (class in core.hooks)": [[44, "core.Hooks.hooks"]], "increment_stats() (hooks method)": [[44, "core.Hooks.hooks.increment_stats"]], "iter (entry attribute)": [[44, "core.Hooks.Entry.iter"]], "level (entry attribute)": [[44, "core.Hooks.Entry.level"]], "logger (hooks attribute)": [[44, "core.Hooks.hooks.logger"]], "meta_data (hooks attribute)": [[44, "core.Hooks.hooks.meta_data"]], "num_restarts (entry attribute)": [[44, "core.Hooks.Entry.num_restarts"]], "post_comm() (hooks method)": [[44, "core.Hooks.hooks.post_comm"]], "post_iteration() (hooks method)": [[44, "core.Hooks.hooks.post_iteration"]], "post_predict() (hooks method)": [[44, "core.Hooks.hooks.post_predict"]], "post_run() (hooks method)": [[44, "core.Hooks.hooks.post_run"]], "post_setup() (hooks method)": [[44, "core.Hooks.hooks.post_setup"]], "post_step() (hooks method)": [[44, "core.Hooks.hooks.post_step"]], "post_sweep() (hooks method)": [[44, "core.Hooks.hooks.post_sweep"]], "pre_comm() (hooks method)": [[44, "core.Hooks.hooks.pre_comm"]], "pre_iteration() (hooks method)": [[44, "core.Hooks.hooks.pre_iteration"]], "pre_predict() (hooks method)": [[44, "core.Hooks.hooks.pre_predict"]], "pre_run() (hooks method)": [[44, "core.Hooks.hooks.pre_run"]], "pre_setup() (hooks method)": 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"core.Lagrange.LagrangeApproximation.getIntegrationMatrix"]], "getinterpolationmatrix() (lagrangeapproximation method)": [[45, "core.Lagrange.LagrangeApproximation.getInterpolationMatrix"]], "n (lagrangeapproximation property)": [[45, "core.Lagrange.LagrangeApproximation.n"]], "points (lagrangeapproximation attribute)": [[45, "core.Lagrange.LagrangeApproximation.points"]], "weights (lagrangeapproximation attribute)": [[45, "core.Lagrange.LagrangeApproximation.weights"]], "core.level": [[46, "module-core.Level"]], "dt (level property)": [[46, "core.Level.level.dt"]], "f (level attribute)": [[46, "core.Level.level.f"]], "fold (level attribute)": [[46, "core.Level.level.fold"]], "level (class in core.level)": [[46, "core.Level.level"]], "level_index (level attribute)": [[46, "core.Level.level.level_index"]], "params (level attribute)": [[46, "core.Level.level.params"]], "prob (level property)": [[46, "core.Level.level.prob"]], "reset_level() (level method)": [[46, "core.Level.level.reset_level"]], "status (level attribute)": [[46, "core.Level.level.status"]], "sweep (level property)": [[46, "core.Level.level.sweep"]], "tag (level property)": [[46, "core.Level.level.tag"]], "tau (level attribute)": [[46, "core.Level.level.tau"]], "time (level property)": [[46, "core.Level.level.time"]], "u (level attribute)": [[46, "core.Level.level.u"]], "uend (level attribute)": [[46, "core.Level.level.uend"]], "uold (level attribute)": [[46, "core.Level.level.uold"]], "nodeserror": [[47, "core.Nodes.NodesError"]], "nodesgenerator (class in core.nodes)": [[47, "core.Nodes.NodesGenerator"]], "core.nodes": [[47, "module-core.Nodes"]], "evalorthogpoly() (nodesgenerator method)": [[47, "core.Nodes.NodesGenerator.evalOrthogPoly"]], "getnodes() (nodesgenerator method)": [[47, "core.Nodes.NodesGenerator.getNodes"]], "getorthogpolycoefficients() (nodesgenerator method)": [[47, "core.Nodes.NodesGenerator.getOrthogPolyCoefficients"]], "gettridiagcoefficients() (nodesgenerator method)": [[47, "core.Nodes.NodesGenerator.getTridiagCoefficients"]], "node_type (nodesgenerator attribute)": [[47, "core.Nodes.NodesGenerator.node_type"]], "quad_type (nodesgenerator attribute)": [[47, "core.Nodes.NodesGenerator.quad_type"]], "workcounter (class in core.problem)": [[48, "core.Problem.WorkCounter"]], "apply_mass_matrix() (ptype method)": [[48, "core.Problem.ptype.apply_mass_matrix"]], "core.problem": [[48, "module-core.Problem"]], "decrement() (workcounter method)": [[48, "core.Problem.WorkCounter.decrement"]], "dtype_f (ptype attribute)": [[48, "core.Problem.ptype.dtype_f"]], "dtype_u (ptype attribute)": [[48, "core.Problem.ptype.dtype_u"]], "eval_f() (ptype method)": [[48, "core.Problem.ptype.eval_f"]], "f_init (ptype property)": [[48, "core.Problem.ptype.f_init"]], "generate_scipy_reference_solution() (ptype method)": [[48, "core.Problem.ptype.generate_scipy_reference_solution"]], "get_default_sweeper_class() (ptype class method)": [[48, "core.Problem.ptype.get_default_sweeper_class"]], "logger (ptype attribute)": [[48, "core.Problem.ptype.logger"], [48, "id0"]], "ptype (class in core.problem)": [[48, "core.Problem.ptype"]], "u_init (ptype property)": [[48, "core.Problem.ptype.u_init"]], "coarse_prob (space_transfer attribute)": [[49, "core.SpaceTransfer.space_transfer.coarse_prob"]], "core.spacetransfer": [[49, "module-core.SpaceTransfer"]], "fine_prob (space_transfer attribute)": [[49, "core.SpaceTransfer.space_transfer.fine_prob"]], "logger (space_transfer attribute)": [[49, "core.SpaceTransfer.space_transfer.logger"]], "params (space_transfer attribute)": [[49, "core.SpaceTransfer.space_transfer.params"]], "prolong() (space_transfer method)": [[49, "core.SpaceTransfer.space_transfer.prolong"]], "restrict() (space_transfer method)": [[49, "core.SpaceTransfer.space_transfer.restrict"]], "space_transfer (class in core.spacetransfer)": [[49, "core.SpaceTransfer.space_transfer"]], "connect_levels() (step method)": [[50, "core.Step.step.connect_levels"]], "core.step": [[50, "module-core.Step"]], "dt (step property)": [[50, "core.Step.step.dt"]], "init_step() (step method)": [[50, "core.Step.step.init_step"]], "levels (step attribute)": [[50, "core.Step.step.levels"]], "logger (step attribute)": [[50, "core.Step.step.logger"]], "next (step property)": [[50, "core.Step.step.next"]], "params (step attribute)": [[50, "core.Step.step.params"]], "prev (step property)": [[50, "core.Step.step.prev"]], "reset_step() (step method)": [[50, "core.Step.step.reset_step"]], "status (step attribute)": [[50, "core.Step.step.status"]], "step (class in core.step)": [[50, "core.Step.step"]], "time (step property)": [[50, "core.Step.step.time"]], "transfer() (step method)": [[50, "core.Step.step.transfer"]], "coll (sweeper attribute)": [[51, "core.Sweeper.sweeper.coll"]], "compute_end_point() (sweeper method)": [[51, "core.Sweeper.sweeper.compute_end_point"]], "compute_residual() (sweeper method)": [[51, "core.Sweeper.sweeper.compute_residual"]], "core.sweeper": [[51, "module-core.Sweeper"]], "get_qdelta_explicit() (sweeper method)": [[51, "core.Sweeper.sweeper.get_Qdelta_explicit"]], "get_qdelta_implicit() (sweeper method)": [[51, "core.Sweeper.sweeper.get_Qdelta_implicit"]], "integrate() (sweeper method)": [[51, "core.Sweeper.sweeper.integrate"]], "level (sweeper property)": [[51, "core.Sweeper.sweeper.level"]], "logger (sweeper attribute)": [[51, "core.Sweeper.sweeper.logger"]], "params (sweeper attribute)": [[51, "core.Sweeper.sweeper.params"]], "predict() (sweeper method)": [[51, "core.Sweeper.sweeper.predict"]], "rank (sweeper property)": [[51, "core.Sweeper.sweeper.rank"]], "sweeper (class in core.sweeper)": [[51, "core.Sweeper.sweeper"]], "update_nodes() (sweeper method)": [[51, "core.Sweeper.sweeper.update_nodes"]], "helpers": [[52, "module-helpers"]], "figsize() (in module helpers.plot_helper)": [[53, "helpers.plot_helper.figsize"]], "figsize_by_journal() (in module helpers.plot_helper)": [[53, "helpers.plot_helper.figsize_by_journal"]], "helpers.plot_helper": [[53, "module-helpers.plot_helper"]], "newfig() (in module helpers.plot_helper)": [[53, "helpers.plot_helper.newfig"]], "savefig() (in module helpers.plot_helper)": [[53, "helpers.plot_helper.savefig"]], "setup_mpl() (in module helpers.plot_helper)": [[53, "helpers.plot_helper.setup_mpl"]], "get_1d_grid() (in module helpers.problem_helper)": [[54, "helpers.problem_helper.get_1d_grid"]], "get_finite_difference_matrix() (in module helpers.problem_helper)": [[54, "helpers.problem_helper.get_finite_difference_matrix"]], "get_finite_difference_stencil() (in module helpers.problem_helper)": [[54, "helpers.problem_helper.get_finite_difference_stencil"]], "get_steps() (in module helpers.problem_helper)": [[54, "helpers.problem_helper.get_steps"]], "helpers.problem_helper": [[54, "module-helpers.problem_helper"]], "frozenclass (class in helpers.pysdc_helper)": [[55, "helpers.pysdc_helper.FrozenClass"]], "__isfrozen (frozenclass attribute)": [[55, "helpers.pysdc_helper.FrozenClass.__isfrozen"]], "get() (frozenclass method)": [[55, "helpers.pysdc_helper.FrozenClass.get"]], "helpers.pysdc_helper": [[55, "module-helpers.pysdc_helper"]], "generate_description() (in module helpers.setup_helper)": [[56, "helpers.setup_helper.generate_description"]], "helpers.setup_helper": [[56, "module-helpers.setup_helper"]], "filter_stats() (in module helpers.stats_helper)": [[57, "helpers.stats_helper.filter_stats"]], "get_list_of_types() (in module helpers.stats_helper)": [[57, "helpers.stats_helper.get_list_of_types"]], "get_sorted() (in module helpers.stats_helper)": [[57, "helpers.stats_helper.get_sorted"]], "helpers.stats_helper": [[57, "module-helpers.stats_helper"]], "sort_stats() (in module helpers.stats_helper)": [[57, "helpers.stats_helper.sort_stats"]], "border_padding() (in module helpers.transfer_helper)": [[58, 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"implementations.controller_classes": [[61, "module-implementations.controller_classes"]], "check_iteration_estimate() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.check_iteration_estimate"]], "controller_mpi (class in implementations.controller_classes.controller_mpi)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI"]], "default() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.default"]], "implementations.controller_classes.controller_mpi": [[62, "module-implementations.controller_classes.controller_MPI"]], "it_check() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.it_check"]], "it_coarse() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.it_coarse"]], "it_down() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.it_down"]], "it_fine() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.it_fine"]], "it_up() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.it_up"]], "pfasst() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.pfasst"]], "predict() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.predict"]], "recv() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.recv"]], "recv_full() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.recv_full"]], "restart_block() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.restart_block"]], "run() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.run"]], "send_full() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.send_full"]], "spread() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.spread"]], "wait_with_interrupt() (controller_mpi method)": [[62, "implementations.controller_classes.controller_MPI.controller_MPI.wait_with_interrupt"]], "controller_nonmpi (class in implementations.controller_classes.controller_nonmpi)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI"]], "default() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.default"]], "implementations.controller_classes.controller_nonmpi": [[63, "module-implementations.controller_classes.controller_nonMPI"]], "it_check() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.it_check"]], "it_coarse() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.it_coarse"]], "it_down() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.it_down"]], "it_fine() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.it_fine"]], "it_up() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.it_up"]], "pfasst() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.pfasst"]], "predict() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.predict"]], "recv_full() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.recv_full"]], "restart_block() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.restart_block"]], "run() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.run"]], "send_full() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.send_full"]], "spread() (controller_nonmpi method)": [[63, "implementations.controller_classes.controller_nonMPI.controller_nonMPI.spread"]], "implementations.convergence_controller_classes": [[64, "module-implementations.convergence_controller_classes"]], "adaptivecollocation (class in implementations.convergence_controller_classes.adaptive_collocation)": [[65, "implementations.convergence_controller_classes.adaptive_collocation.AdaptiveCollocation"]], "check_parameters() (adaptivecollocation method)": [[65, "implementations.convergence_controller_classes.adaptive_collocation.AdaptiveCollocation.check_parameters"]], "implementations.convergence_controller_classes.adaptive_collocation": [[65, "module-implementations.convergence_controller_classes.adaptive_collocation"]], "matmul() (adaptivecollocation method)": [[65, "implementations.convergence_controller_classes.adaptive_collocation.AdaptiveCollocation.matmul"]], "post_iteration_processing() (adaptivecollocation method)": [[65, "implementations.convergence_controller_classes.adaptive_collocation.AdaptiveCollocation.post_iteration_processing"]], "post_spread_processing() (adaptivecollocation method)": [[65, "implementations.convergence_controller_classes.adaptive_collocation.AdaptiveCollocation.post_spread_processing"]], "reset_status_variables() (adaptivecollocation method)": [[65, "implementations.convergence_controller_classes.adaptive_collocation.AdaptiveCollocation.reset_status_variables"]], "setup() (adaptivecollocation method)": 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(class in implementations.convergence_controller_classes.adaptivity)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityExtrapolationWithinQ"]], "adaptivityforconvergedcollocationproblems (class in implementations.convergence_controller_classes.adaptivity)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityForConvergedCollocationProblems"]], "adaptivitypolynomialerror (class in implementations.convergence_controller_classes.adaptivity)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityPolynomialError"]], "adaptivityrk (class in implementations.convergence_controller_classes.adaptivity)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityRK"]], "adaptivityresidual (class in implementations.convergence_controller_classes.adaptivity)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityResidual"]], "check_parameters() (adaptivity method)": [[66, "implementations.convergence_controller_classes.adaptivity.Adaptivity.check_parameters"]], "check_parameters() (adaptivitycollocation method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityCollocation.check_parameters"]], "check_parameters() (adaptivityresidual method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityResidual.check_parameters"]], "compute_optimal_step_size() (adaptivitybase method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityBase.compute_optimal_step_size"]], "dependencies() (adaptivity method)": [[66, "implementations.convergence_controller_classes.adaptivity.Adaptivity.dependencies"]], "dependencies() (adaptivitybase method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityBase.dependencies"]], "dependencies() (adaptivitycollocation method)": [[66, "implementations.convergence_controller_classes.adaptivity.AdaptivityCollocation.dependencies"]], 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"implementations.problem_classes.PenningTrap_3D.penningtrap.u_exact"]], "u_init() (penningtrap method)": [[122, "implementations.problem_classes.PenningTrap_3D.penningtrap.u_init"]], "work_counter (penningtrap attribute)": [[122, "implementations.problem_classes.PenningTrap_3D.penningtrap.work_counter"]], "dtype_f (piline attribute)": [[123, "implementations.problem_classes.Piline.piline.dtype_f"]], "dtype_u (piline attribute)": [[123, "implementations.problem_classes.Piline.piline.dtype_u"]], "eval_f() (piline method)": [[123, "implementations.problem_classes.Piline.piline.eval_f"]], "implementations.problem_classes.piline": [[123, "module-implementations.problem_classes.Piline"]], "piline (class in implementations.problem_classes.piline)": [[123, "implementations.problem_classes.Piline.piline"]], "solve_system() (piline method)": [[123, "implementations.problem_classes.Piline.piline.solve_system"]], "u_exact() (piline method)": [[123, "implementations.problem_classes.Piline.piline.u_exact"]], "a (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.A"]], "id (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.Id"]], "quench (class in implementations.problem_classes.quench)": [[124, "implementations.problem_classes.Quench.Quench"]], "quenchimex (class in implementations.problem_classes.quench)": [[124, "implementations.problem_classes.Quench.QuenchIMEX"]], "dtype_f (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.dtype_f"]], "dtype_f (quenchimex attribute)": [[124, "implementations.problem_classes.Quench.QuenchIMEX.dtype_f"]], "dtype_u (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.dtype_u"]], "dx (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.dx"]], "eval_f() (quench method)": [[124, "implementations.problem_classes.Quench.Quench.eval_f"]], "eval_f() (quenchimex method)": [[124, "implementations.problem_classes.Quench.QuenchIMEX.eval_f"]], "eval_f_non_linear() (quench method)": [[124, "implementations.problem_classes.Quench.Quench.eval_f_non_linear"]], "get_non_linear_jacobian() (quench method)": [[124, "implementations.problem_classes.Quench.Quench.get_non_linear_Jacobian"]], "implementations.problem_classes.quench": [[124, "module-implementations.problem_classes.Quench"]], "leak (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.leak"]], "solve_system() (quench method)": [[124, "implementations.problem_classes.Quench.Quench.solve_system"]], "solve_system() (quenchimex method)": [[124, "implementations.problem_classes.Quench.QuenchIMEX.solve_system"]], "u_exact() (quench method)": [[124, "implementations.problem_classes.Quench.Quench.u_exact"]], "u_exact() (quenchimex method)": [[124, "implementations.problem_classes.Quench.QuenchIMEX.u_exact"]], "xv (quench attribute)": [[124, "implementations.problem_classes.Quench.Quench.xv"]], "a (testequation0d attribute)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d.A"]], "dtype_f (testequation0d attribute)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d.dtype_f"]], "dtype_u (testequation0d attribute)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d.dtype_u"]], "eval_f() (testequation0d method)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d.eval_f"]], "implementations.problem_classes.testequation_0d": [[125, "module-implementations.problem_classes.TestEquation_0D"]], "solve_system() (testequation0d method)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d.solve_system"]], "testequation0d (class in implementations.problem_classes.testequation_0d)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d"]], "u_exact() (testequation0d method)": [[125, "implementations.problem_classes.TestEquation_0D.testequation0d.u_exact"]], "dtype_f (vanderpol attribute)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol.dtype_f"]], "dtype_u (vanderpol attribute)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol.dtype_u"]], "eval_f() (vanderpol method)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol.eval_f"]], "implementations.problem_classes.van_der_pol_implicit": [[126, "module-implementations.problem_classes.Van_der_Pol_implicit"]], "solve_system() (vanderpol method)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol.solve_system"]], "u_exact() (vanderpol method)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol.u_exact"]], "vanderpol (class in implementations.problem_classes.van_der_pol_implicit)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol"]], "work_counters (vanderpol attribute)": [[126, "implementations.problem_classes.Van_der_Pol_implicit.vanderpol.work_counters"]], "k (fenics_vortex_2d attribute)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.K"]], "m (fenics_vortex_2d attribute)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.M"]], "v (fenics_vortex_2d attribute)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.V"]], "dtype_f (fenics_vortex_2d attribute)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.dtype_f"]], "dtype_u (fenics_vortex_2d attribute)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.dtype_u"]], "eval_f() (fenics_vortex_2d method)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.eval_f"]], "fenics_vortex_2d (class in implementations.problem_classes.vorticityvelocity_2d_fenics_periodic)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d"]], "implementations.problem_classes.vorticityvelocity_2d_fenics_periodic": [[127, "module-implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic"]], "solve_system() (fenics_vortex_2d method)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.solve_system"]], "u_exact() (fenics_vortex_2d method)": [[127, "implementations.problem_classes.VorticityVelocity_2D_FEniCS_periodic.fenics_vortex_2d.u_exact"]], "implementations.problem_classes.acoustic_helpers": [[128, "module-implementations.problem_classes.acoustic_helpers"]], "getbcleft() (in module implementations.problem_classes.acoustic_helpers.buildfdmatrix)": [[129, "implementations.problem_classes.acoustic_helpers.buildFDMatrix.getBCLeft"]], "getbcright() (in module implementations.problem_classes.acoustic_helpers.buildfdmatrix)": [[129, "implementations.problem_classes.acoustic_helpers.buildFDMatrix.getBCRight"]], "gethorizontaldx() (in module implementations.problem_classes.acoustic_helpers.buildfdmatrix)": [[129, "implementations.problem_classes.acoustic_helpers.buildFDMatrix.getHorizontalDx"]], "getmatrix() (in module implementations.problem_classes.acoustic_helpers.buildfdmatrix)": [[129, "implementations.problem_classes.acoustic_helpers.buildFDMatrix.getMatrix"]], "implementations.problem_classes.acoustic_helpers.buildfdmatrix": [[129, "module-implementations.problem_classes.acoustic_helpers.buildFDMatrix"]], "getwave1dadvectionmatrix() (in module implementations.problem_classes.acoustic_helpers.buildwave1dmatrix)": [[130, "implementations.problem_classes.acoustic_helpers.buildWave1DMatrix.getWave1DAdvectionMatrix"]], "getwave1dmatrix() (in module implementations.problem_classes.acoustic_helpers.buildwave1dmatrix)": [[130, "implementations.problem_classes.acoustic_helpers.buildWave1DMatrix.getWave1DMatrix"]], "getwavebcleft() (in module implementations.problem_classes.acoustic_helpers.buildwave1dmatrix)": [[130, "implementations.problem_classes.acoustic_helpers.buildWave1DMatrix.getWaveBCLeft"]], "getwavebcright() (in module implementations.problem_classes.acoustic_helpers.buildwave1dmatrix)": [[130, "implementations.problem_classes.acoustic_helpers.buildWave1DMatrix.getWaveBCRight"]], "implementations.problem_classes.acoustic_helpers.buildwave1dmatrix": [[130, "module-implementations.problem_classes.acoustic_helpers.buildWave1DMatrix"]], "bdf2 (class in implementations.problem_classes.acoustic_helpers.standard_integrators)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.bdf2"]], "dirk (class in implementations.problem_classes.acoustic_helpers.standard_integrators)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.dirk"]], "f() (dirk method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.dirk.f"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.dirk.f"]], "f_fast() (rk_imex method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.rk_imex.f_fast"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.rk_imex.f_fast"]], "f_fast_solve() (rk_imex method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.rk_imex.f_fast_solve"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.rk_imex.f_fast_solve"]], "f_slow() (rk_imex method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.rk_imex.f_slow"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.rk_imex.f_slow"]], "f_solve() (dirk method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.dirk.f_solve"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.dirk.f_solve"]], "firsttimestep() (bdf2 method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.bdf2.firsttimestep"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.bdf2.firsttimestep"]], "implementations.problem_classes.acoustic_helpers.standard_integrators": [[131, "module-implementations.problem_classes.acoustic_helpers.standard_integrators"]], "rk_imex (class in implementations.problem_classes.acoustic_helpers.standard_integrators)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.rk_imex"]], "timestep() (bdf2 method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.bdf2.timestep"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.bdf2.timestep"]], "timestep() (dirk method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.dirk.timestep"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.dirk.timestep"]], "timestep() (rk_imex method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.rk_imex.timestep"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.rk_imex.timestep"]], "timestep() (trapezoidal method)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.trapezoidal.timestep"], [137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.trapezoidal.timestep"]], "trapezoidal (class in implementations.problem_classes.acoustic_helpers.standard_integrators)": [[131, "implementations.problem_classes.acoustic_helpers.standard_integrators.trapezoidal"]], "implementations.problem_classes.boussinesq_helpers": [[132, "module-implementations.problem_classes.boussinesq_helpers"]], "get2dmatrix() (in module implementations.problem_classes.boussinesq_helpers.build2dfdmatrix)": [[133, "implementations.problem_classes.boussinesq_helpers.build2DFDMatrix.get2DMatrix"]], "get2dmesh() (in module implementations.problem_classes.boussinesq_helpers.build2dfdmatrix)": [[133, "implementations.problem_classes.boussinesq_helpers.build2DFDMatrix.get2DMesh"]], "get2dupwindmatrix() (in module implementations.problem_classes.boussinesq_helpers.build2dfdmatrix)": [[133, "implementations.problem_classes.boussinesq_helpers.build2DFDMatrix.get2DUpwindMatrix"]], "getbchorizontal() (in module implementations.problem_classes.boussinesq_helpers.build2dfdmatrix)": [[133, "implementations.problem_classes.boussinesq_helpers.build2DFDMatrix.getBCHorizontal"]], "getbcvertical() (in module implementations.problem_classes.boussinesq_helpers.build2dfdmatrix)": [[133, "implementations.problem_classes.boussinesq_helpers.build2DFDMatrix.getBCVertical"]], "implementations.problem_classes.boussinesq_helpers.build2dfdmatrix": [[133, "module-implementations.problem_classes.boussinesq_helpers.build2DFDMatrix"]], "getboussinesq2dmatrix() (in module implementations.problem_classes.boussinesq_helpers.buildboussinesq2dmatrix)": [[134, "implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix.getBoussinesq2DMatrix"]], "getboussinesq2dupwindmatrix() (in module implementations.problem_classes.boussinesq_helpers.buildboussinesq2dmatrix)": [[134, "implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix.getBoussinesq2DUpwindMatrix"]], "getboussinesqbchorizontal() (in module implementations.problem_classes.boussinesq_helpers.buildboussinesq2dmatrix)": [[134, "implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix.getBoussinesqBCHorizontal"]], "getboussinesqbcvertical() (in module implementations.problem_classes.boussinesq_helpers.buildboussinesq2dmatrix)": [[134, "implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix.getBoussinesqBCVertical"]], "implementations.problem_classes.boussinesq_helpers.buildboussinesq2dmatrix": [[134, "module-implementations.problem_classes.boussinesq_helpers.buildBoussinesq2DMatrix"]], "getbcleft() (in module implementations.problem_classes.boussinesq_helpers.buildfdmatrix)": [[135, "implementations.problem_classes.boussinesq_helpers.buildFDMatrix.getBCLeft"]], "getbcright() (in module implementations.problem_classes.boussinesq_helpers.buildfdmatrix)": [[135, "implementations.problem_classes.boussinesq_helpers.buildFDMatrix.getBCRight"]], "getmatrix() (in module implementations.problem_classes.boussinesq_helpers.buildfdmatrix)": [[135, "implementations.problem_classes.boussinesq_helpers.buildFDMatrix.getMatrix"]], "getupwindmatrix() (in module implementations.problem_classes.boussinesq_helpers.buildfdmatrix)": [[135, "implementations.problem_classes.boussinesq_helpers.buildFDMatrix.getUpwindMatrix"]], "implementations.problem_classes.boussinesq_helpers.buildfdmatrix": [[135, "module-implementations.problem_classes.boussinesq_helpers.buildFDMatrix"]], "callback (class in implementations.problem_classes.boussinesq_helpers.helper_classes)": [[136, "implementations.problem_classes.boussinesq_helpers.helper_classes.Callback"]], "add() (logging method)": [[136, "implementations.problem_classes.boussinesq_helpers.helper_classes.logging.add"]], "getcounter() (callback method)": [[136, "implementations.problem_classes.boussinesq_helpers.helper_classes.Callback.getcounter"]], "getresidual() (callback method)": [[136, "implementations.problem_classes.boussinesq_helpers.helper_classes.Callback.getresidual"]], "implementations.problem_classes.boussinesq_helpers.helper_classes": [[136, "module-implementations.problem_classes.boussinesq_helpers.helper_classes"]], "logging (class in implementations.problem_classes.boussinesq_helpers.helper_classes)": [[136, "implementations.problem_classes.boussinesq_helpers.helper_classes.logging"]], "numsmalltimesteps() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.NumSmallTimeSteps"]], "rk3lin() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.RK3Lin"]], "splitexplicit (class in implementations.problem_classes.boussinesq_helpers.standard_integrators)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit"]], "verletlin() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.VerletLin"]], "bdf2 (class in implementations.problem_classes.boussinesq_helpers.standard_integrators)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.bdf2"]], "dirk (class in implementations.problem_classes.boussinesq_helpers.standard_integrators)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.dirk"]], "f() (bdf2 method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.bdf2.f"]], "f() (trapezoidal method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.trapezoidal.f"]], "f_fast() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.f_fast"]], "f_fastmom() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.f_fastMom"]], "f_fastther() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.f_fastTher"]], "f_slow() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.f_slow"]], "f_solve() (bdf2 method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.bdf2.f_solve"]], "f_solve() (trapezoidal method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.trapezoidal.f_solve"]], "implementations.problem_classes.boussinesq_helpers.standard_integrators": [[137, "module-implementations.problem_classes.boussinesq_helpers.standard_integrators"]], "rk_imex (class in implementations.problem_classes.boussinesq_helpers.standard_integrators)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.rk_imex"]], "timestep() (splitexplicit method)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.SplitExplicit.timestep"]], "trapezoidal (class in implementations.problem_classes.boussinesq_helpers.standard_integrators)": [[137, "implementations.problem_classes.boussinesq_helpers.standard_integrators.trapezoidal"]], "implementations.problem_classes.boussinesq_helpers.unflatten": [[138, "module-implementations.problem_classes.boussinesq_helpers.unflatten"]], "unflatten() (in module implementations.problem_classes.boussinesq_helpers.unflatten)": [[138, "implementations.problem_classes.boussinesq_helpers.unflatten.unflatten"]], "a (genericndimfindiff attribute)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.A"]], "genericndimfindiff (class in implementations.problem_classes.generic_nd_fd)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff"]], "id (genericndimfindiff attribute)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.Id"]], "dtype_f (genericndimfindiff attribute)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.dtype_f"]], "dtype_u (genericndimfindiff attribute)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.dtype_u"]], "dx (genericndimfindiff property)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.dx"]], "eval_f() (genericndimfindiff method)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.eval_f"]], "get_default_sweeper_class() (genericndimfindiff class method)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.get_default_sweeper_class"]], "grids (genericndimfindiff property)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.grids"]], "implementations.problem_classes.generic_nd_fd": [[139, "module-implementations.problem_classes.generic_ND_FD"]], "ndim (genericndimfindiff property)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.ndim"]], "solve_system() (genericndimfindiff method)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.solve_system"]], "xvalues (genericndimfindiff attribute)": [[139, "implementations.problem_classes.generic_ND_FD.GenericNDimFinDiff.xvalues"]], "dtype_f (nonlinear_ode_1 attribute)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.dtype_f"]], "dtype_u (nonlinear_ode_1 attribute)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.dtype_u"]], "eval_f() (nonlinear_ode_1 method)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.eval_f"]], "implementations.problem_classes.nonlinear_ode_1": [[140, "module-implementations.problem_classes.nonlinear_ODE_1"]], "newton_itercount (nonlinear_ode_1 attribute)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.newton_itercount"]], "newton_ncalls (nonlinear_ode_1 attribute)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.newton_ncalls"]], "nonlinear_ode_1 (class in implementations.problem_classes.nonlinear_ode_1)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1"]], "solve_system() (nonlinear_ode_1 method)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.solve_system"]], "u_exact() (nonlinear_ode_1 method)": [[140, "implementations.problem_classes.nonlinear_ODE_1.nonlinear_ODE_1.u_exact"]], "dtype_f (polynomial_testequation attribute)": [[141, "implementations.problem_classes.polynomial_test_problem.polynomial_testequation.dtype_f"]], "dtype_f (polynomial_testequation_imex attribute)": [[141, "implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX.dtype_f"]], "dtype_u (polynomial_testequation attribute)": [[141, "implementations.problem_classes.polynomial_test_problem.polynomial_testequation.dtype_u"]], "eval_f() (polynomial_testequation method)": [[141, "implementations.problem_classes.polynomial_test_problem.polynomial_testequation.eval_f"]], "eval_f() (polynomial_testequation_imex method)": [[141, "implementations.problem_classes.polynomial_test_problem.polynomial_testequation_IMEX.eval_f"]], "implementations.problem_classes.polynomial_test_problem": [[141, "module-implementations.problem_classes.polynomial_test_problem"]], "polynomial_testequation (class in 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"implementations.sweeper_classes.generic_implicit_MPI.SweeperMPI.compute_end_point"]], "compute_end_point() (generic_implicit_mpi method)": [[149, "implementations.sweeper_classes.generic_implicit_MPI.generic_implicit_MPI.compute_end_point"]], "compute_residual() (sweepermpi method)": [[149, "implementations.sweeper_classes.generic_implicit_MPI.SweeperMPI.compute_residual"]], "generic_implicit_mpi (class in implementations.sweeper_classes.generic_implicit_mpi)": [[149, "implementations.sweeper_classes.generic_implicit_MPI.generic_implicit_MPI"]], "implementations.sweeper_classes.generic_implicit_mpi": [[149, "module-implementations.sweeper_classes.generic_implicit_MPI"]], "integrate() (generic_implicit_mpi method)": [[149, "implementations.sweeper_classes.generic_implicit_MPI.generic_implicit_MPI.integrate"]], "predict() (sweepermpi method)": [[149, "implementations.sweeper_classes.generic_implicit_MPI.SweeperMPI.predict"]], "rank (sweepermpi property)": [[149, "implementations.sweeper_classes.generic_implicit_MPI.SweeperMPI.rank"]], "rank (generic_implicit_mpi attribute)": [[149, "implementations.sweeper_classes.generic_implicit_MPI.generic_implicit_MPI.rank"]], "update_nodes() (generic_implicit_mpi method)": [[149, "implementations.sweeper_classes.generic_implicit_MPI.generic_implicit_MPI.update_nodes"]], "qe (imex_1st_order attribute)": [[150, "implementations.sweeper_classes.imex_1st_order.imex_1st_order.QE"]], "qi (imex_1st_order attribute)": [[150, "implementations.sweeper_classes.imex_1st_order.imex_1st_order.QI"]], "compute_end_point() (imex_1st_order method)": [[150, "implementations.sweeper_classes.imex_1st_order.imex_1st_order.compute_end_point"]], "get_scalar_problems_manysweep_mat() (imex_1st_order method)": [[150, "implementations.sweeper_classes.imex_1st_order.imex_1st_order.get_scalar_problems_manysweep_mat"]], "get_scalar_problems_sweeper_mats() (imex_1st_order method)": [[150, "implementations.sweeper_classes.imex_1st_order.imex_1st_order.get_scalar_problems_sweeper_mats"]], "get_sweeper_mats() (imex_1st_order method)": [[150, "implementations.sweeper_classes.imex_1st_order.imex_1st_order.get_sweeper_mats"]], "imex_1st_order (class in implementations.sweeper_classes.imex_1st_order)": [[150, "implementations.sweeper_classes.imex_1st_order.imex_1st_order"]], "implementations.sweeper_classes.imex_1st_order": [[150, "module-implementations.sweeper_classes.imex_1st_order"]], "integrate() (imex_1st_order method)": [[150, "implementations.sweeper_classes.imex_1st_order.imex_1st_order.integrate"]], "update_nodes() (imex_1st_order method)": [[150, "implementations.sweeper_classes.imex_1st_order.imex_1st_order.update_nodes"]], "compute_end_point() (imex_1st_order_mpi method)": [[151, "implementations.sweeper_classes.imex_1st_order_MPI.imex_1st_order_MPI.compute_end_point"]], "imex_1st_order_mpi (class in implementations.sweeper_classes.imex_1st_order_mpi)": [[151, "implementations.sweeper_classes.imex_1st_order_MPI.imex_1st_order_MPI"]], "implementations.sweeper_classes.imex_1st_order_mpi": [[151, "module-implementations.sweeper_classes.imex_1st_order_MPI"]], "integrate() (imex_1st_order_mpi method)": [[151, "implementations.sweeper_classes.imex_1st_order_MPI.imex_1st_order_MPI.integrate"]], "update_nodes() (imex_1st_order_mpi method)": [[151, "implementations.sweeper_classes.imex_1st_order_MPI.imex_1st_order_MPI.update_nodes"]], "compute_end_point() (imex_1st_order_mass method)": [[152, "implementations.sweeper_classes.imex_1st_order_mass.imex_1st_order_mass.compute_end_point"]], "compute_residual() (imex_1st_order_mass method)": [[152, "implementations.sweeper_classes.imex_1st_order_mass.imex_1st_order_mass.compute_residual"]], "imex_1st_order_mass (class in implementations.sweeper_classes.imex_1st_order_mass)": [[152, "implementations.sweeper_classes.imex_1st_order_mass.imex_1st_order_mass"]], "implementations.sweeper_classes.imex_1st_order_mass": [[152, "module-implementations.sweeper_classes.imex_1st_order_mass"]], "update_nodes() (imex_1st_order_mass method)": [[152, "implementations.sweeper_classes.imex_1st_order_mass.imex_1st_order_mass.update_nodes"]], "q1 (multi_implicit attribute)": [[153, "implementations.sweeper_classes.multi_implicit.multi_implicit.Q1"]], "q2 (multi_implicit attribute)": [[153, "implementations.sweeper_classes.multi_implicit.multi_implicit.Q2"]], "compute_end_point() (multi_implicit method)": [[153, "implementations.sweeper_classes.multi_implicit.multi_implicit.compute_end_point"]], "implementations.sweeper_classes.multi_implicit": [[153, "module-implementations.sweeper_classes.multi_implicit"]], "integrate() (multi_implicit method)": [[153, "implementations.sweeper_classes.multi_implicit.multi_implicit.integrate"]], "multi_implicit (class in implementations.sweeper_classes.multi_implicit)": [[153, "implementations.sweeper_classes.multi_implicit.multi_implicit"]], "update_nodes() (multi_implicit method)": [[153, "implementations.sweeper_classes.multi_implicit.multi_implicit.update_nodes"]], "qq (verlet attribute)": [[154, "implementations.sweeper_classes.verlet.verlet.QQ"], [154, "implementations.sweeper_classes.verlet.verlet.qQ"]], "qt (verlet attribute)": [[154, "implementations.sweeper_classes.verlet.verlet.QT"]], "qx (verlet attribute)": [[154, "implementations.sweeper_classes.verlet.verlet.Qx"]], "compute_end_point() (verlet method)": [[154, "implementations.sweeper_classes.verlet.verlet.compute_end_point"]], "implementations.sweeper_classes.verlet": [[154, "module-implementations.sweeper_classes.verlet"]], "integrate() (verlet method)": [[154, "implementations.sweeper_classes.verlet.verlet.integrate"]], "update_nodes() (verlet method)": [[154, "implementations.sweeper_classes.verlet.verlet.update_nodes"]], "verlet (class in implementations.sweeper_classes.verlet)": [[154, "implementations.sweeper_classes.verlet.verlet"]], "implementations.transfer_classes": [[155, "module-implementations.transfer_classes"]], "base_transfer_mass (class in implementations.transfer_classes.basetransfer_mass)": [[156, "implementations.transfer_classes.BaseTransfer_mass.base_transfer_mass"]], "coarse (base_transfer_mass attribute)": [[156, "implementations.transfer_classes.BaseTransfer_mass.base_transfer_mass.coarse"]], "fine (base_transfer_mass attribute)": [[156, "implementations.transfer_classes.BaseTransfer_mass.base_transfer_mass.fine"]], "implementations.transfer_classes.basetransfer_mass": [[156, "module-implementations.transfer_classes.BaseTransfer_mass"]], "logger (base_transfer_mass attribute)": [[156, "implementations.transfer_classes.BaseTransfer_mass.base_transfer_mass.logger"]], "params (base_transfer_mass attribute)": [[156, "implementations.transfer_classes.BaseTransfer_mass.base_transfer_mass.params"]], "prolong() (base_transfer_mass method)": [[156, "implementations.transfer_classes.BaseTransfer_mass.base_transfer_mass.prolong"]], "prolong_f() (base_transfer_mass method)": [[156, "implementations.transfer_classes.BaseTransfer_mass.base_transfer_mass.prolong_f"]], "restrict() (base_transfer_mass method)": [[156, "implementations.transfer_classes.BaseTransfer_mass.base_transfer_mass.restrict"]], "implementations.transfer_classes.transferfenicsmesh": [[157, "module-implementations.transfer_classes.TransferFenicsMesh"]], "mesh_to_mesh_fenics (class in implementations.transfer_classes.transferfenicsmesh)": [[157, "implementations.transfer_classes.TransferFenicsMesh.mesh_to_mesh_fenics"]], "project() (mesh_to_mesh_fenics method)": [[157, "implementations.transfer_classes.TransferFenicsMesh.mesh_to_mesh_fenics.project"]], "prolong() (mesh_to_mesh_fenics method)": [[157, "implementations.transfer_classes.TransferFenicsMesh.mesh_to_mesh_fenics.prolong"]], "restrict() (mesh_to_mesh_fenics method)": [[157, "implementations.transfer_classes.TransferFenicsMesh.mesh_to_mesh_fenics.restrict"]], "pspace (mesh_to_mesh attribute)": [[158, "implementations.transfer_classes.TransferMesh.mesh_to_mesh.Pspace"], [162, "implementations.transfer_classes.TransferMesh_NoCoarse.mesh_to_mesh.Pspace"]], "rspace (mesh_to_mesh attribute)": [[158, "implementations.transfer_classes.TransferMesh.mesh_to_mesh.Rspace"], [162, "implementations.transfer_classes.TransferMesh_NoCoarse.mesh_to_mesh.Rspace"]], "implementations.transfer_classes.transfermesh": [[158, "module-implementations.transfer_classes.TransferMesh"]], "mesh_to_mesh (class in implementations.transfer_classes.transfermesh)": [[158, "implementations.transfer_classes.TransferMesh.mesh_to_mesh"]], "prolong() (mesh_to_mesh method)": [[158, "implementations.transfer_classes.TransferMesh.mesh_to_mesh.prolong"], [162, "implementations.transfer_classes.TransferMesh_NoCoarse.mesh_to_mesh.prolong"]], "restrict() (mesh_to_mesh method)": [[158, "implementations.transfer_classes.TransferMesh.mesh_to_mesh.restrict"], [162, "implementations.transfer_classes.TransferMesh_NoCoarse.mesh_to_mesh.restrict"]], "implementations.transfer_classes.transfermesh_fft": [[159, "module-implementations.transfer_classes.TransferMesh_FFT"]], "irfft_object_fine (mesh_to_mesh_fft attribute)": [[159, "implementations.transfer_classes.TransferMesh_FFT.mesh_to_mesh_fft.irfft_object_fine"]], "mesh_to_mesh_fft (class in implementations.transfer_classes.transfermesh_fft)": [[159, "implementations.transfer_classes.TransferMesh_FFT.mesh_to_mesh_fft"]], "prolong() (mesh_to_mesh_fft method)": [[159, "implementations.transfer_classes.TransferMesh_FFT.mesh_to_mesh_fft.prolong"]], "restrict() (mesh_to_mesh_fft method)": [[159, "implementations.transfer_classes.TransferMesh_FFT.mesh_to_mesh_fft.restrict"]], "rfft_object_coarse (mesh_to_mesh_fft attribute)": [[159, "implementations.transfer_classes.TransferMesh_FFT.mesh_to_mesh_fft.rfft_object_coarse"]], "pspace (mesh_to_mesh_fft2d attribute)": [[160, "implementations.transfer_classes.TransferMesh_FFT2D.mesh_to_mesh_fft2d.Pspace"]], "rspace (mesh_to_mesh_fft2d attribute)": [[160, "implementations.transfer_classes.TransferMesh_FFT2D.mesh_to_mesh_fft2d.Rspace"]], "implementations.transfer_classes.transfermesh_fft2d": [[160, "module-implementations.transfer_classes.TransferMesh_FFT2D"]], "mesh_to_mesh_fft2d (class in implementations.transfer_classes.transfermesh_fft2d)": [[160, "implementations.transfer_classes.TransferMesh_FFT2D.mesh_to_mesh_fft2d"]], "prolong() (mesh_to_mesh_fft2d method)": [[160, "implementations.transfer_classes.TransferMesh_FFT2D.mesh_to_mesh_fft2d.prolong"]], "restrict() (mesh_to_mesh_fft2d method)": [[160, "implementations.transfer_classes.TransferMesh_FFT2D.mesh_to_mesh_fft2d.restrict"]], "fft_to_fft (class in implementations.transfer_classes.transfermesh_mpifft)": [[161, "implementations.transfer_classes.TransferMesh_MPIFFT.fft_to_fft"]], "implementations.transfer_classes.transfermesh_mpifft": [[161, "module-implementations.transfer_classes.TransferMesh_MPIFFT"]], "prolong() (fft_to_fft method)": [[161, "implementations.transfer_classes.TransferMesh_MPIFFT.fft_to_fft.prolong"]], "restrict() (fft_to_fft method)": [[161, "implementations.transfer_classes.TransferMesh_MPIFFT.fft_to_fft.restrict"]], "implementations.transfer_classes.transfermesh_nocoarse": [[162, "module-implementations.transfer_classes.TransferMesh_NoCoarse"]], "mesh_to_mesh (class in implementations.transfer_classes.transfermesh_nocoarse)": [[162, "implementations.transfer_classes.TransferMesh_NoCoarse.mesh_to_mesh"]], "implementations.transfer_classes.transferpetscdmda": [[163, "module-implementations.transfer_classes.TransferPETScDMDA"]], "mesh_to_mesh_petsc_dmda (class in implementations.transfer_classes.transferpetscdmda)": [[163, "implementations.transfer_classes.TransferPETScDMDA.mesh_to_mesh_petsc_dmda"]], "prolong() (mesh_to_mesh_petsc_dmda method)": [[163, "implementations.transfer_classes.TransferPETScDMDA.mesh_to_mesh_petsc_dmda.prolong"]], "restrict() (mesh_to_mesh_petsc_dmda method)": [[163, "implementations.transfer_classes.TransferPETScDMDA.mesh_to_mesh_petsc_dmda.restrict"]], "implementations.transfer_classes.transferparticles_nocoarse": [[164, "module-implementations.transfer_classes.TransferParticles_NoCoarse"]], "particles_to_particles (class in implementations.transfer_classes.transferparticles_nocoarse)": [[164, "implementations.transfer_classes.TransferParticles_NoCoarse.particles_to_particles"]], "prolong() (particles_to_particles method)": [[164, "implementations.transfer_classes.TransferParticles_NoCoarse.particles_to_particles.prolong"]], "restrict() (particles_to_particles method)": [[164, "implementations.transfer_classes.TransferParticles_NoCoarse.particles_to_particles.restrict"]]}})
\ No newline at end of file
diff --git a/tutorial/doc_step_2_C.html b/tutorial/doc_step_2_C.html
index cb5621a336..dc27c54526 100644
--- a/tutorial/doc_step_2_C.html
+++ b/tutorial/doc_step_2_C.html
@@ -118,7 +118,7 @@ <h3>Navigation</h3>
 </pre></div>
 </div>
 <p>Results:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>2023-11-09 08:47:26,112 - controller - Controller - welcome_message - 146 - INFO: Welcome to the one and only, really very astonishing and 87.3% bug free
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>2023-11-10 06:55:51,312 - controller - Controller - welcome_message - 146 - INFO: Welcome to the one and only, really very astonishing and 87.3% bug free
                                  _____ _____   _____ 
                                 / ____|  __ \ / ____|
                     _ __  _   _| (___ | |  | | |     
@@ -128,8 +128,8 @@ <h3>Navigation</h3>
                    | |     __/ |                     
                    |_|    |___/                      
                                                      
-2023-11-09 08:47:26,112 - controller - Controller - dump_setup - 160 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- BEGIN
-2023-11-09 08:47:26,113 - controller - Controller - dump_setup - 227 - INFO: ----------------------------------------------------------------------------------------------------
+2023-11-10 06:55:51,312 - controller - Controller - dump_setup - 160 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- BEGIN
+2023-11-10 06:55:51,313 - controller - Controller - dump_setup - 227 - INFO: ----------------------------------------------------------------------------------------------------
 
 Controller: &lt;class &#39;pySDC.implementations.controller_classes.controller_nonMPI.controller_nonMPI&#39;&gt;
     all_to_done = False
@@ -182,34 +182,34 @@ <h3>Navigation</h3>
  -&gt; |  1 |   100 | SpreadStepSizesBlockwiseNonMPI
     |  2 |   200 | CheckConvergence
 
-2023-11-09 08:47:26,113 - controller - Controller - dump_setup - 230 - INFO: ----------------------------------------------------------------------------------------------------
-2023-11-09 08:47:26,113 - controller - Controller - dump_setup - 232 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- END
+2023-11-10 06:55:51,313 - controller - Controller - dump_setup - 230 - INFO: ----------------------------------------------------------------------------------------------------
+2023-11-10 06:55:51,313 - controller - Controller - dump_setup - 232 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- END
 
-2023-11-09 08:47:26,117 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  1 -- Sweep:  1 -- residual: 4.11190756e-03
-2023-11-09 08:47:26,121 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  2 -- Sweep:  1 -- residual: 6.68442665e-04
-2023-11-09 08:47:26,125 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  3 -- Sweep:  1 -- residual: 8.80377586e-05
-2023-11-09 08:47:26,129 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  4 -- Sweep:  1 -- residual: 1.21707912e-05
-2023-11-09 08:47:26,133 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  5 -- Sweep:  1 -- residual: 1.38272106e-06
-2023-11-09 08:47:26,137 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  6 -- Sweep:  1 -- residual: 6.36444759e-07
-2023-11-09 08:47:26,141 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  7 -- Sweep:  1 -- residual: 1.68953978e-07
-2023-11-09 08:47:26,145 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  8 -- Sweep:  1 -- residual: 3.52597535e-08
-2023-11-09 08:47:26,149 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  9 -- Sweep:  1 -- residual: 6.07222841e-09
-2023-11-09 08:47:26,153 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration: 10 -- Sweep:  1 -- residual: 8.28029601e-10
-2023-11-09 08:47:26,157 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration: 11 -- Sweep:  1 -- residual: 1.19626442e-10
-2023-11-09 08:47:26,161 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration: 12 -- Sweep:  1 -- residual: 1.44777350e-11
-2023-11-09 08:47:26,166 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  1 -- Sweep:  1 -- residual: 6.69984764e-03
-2023-11-09 08:47:26,170 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  2 -- Sweep:  1 -- residual: 1.05518433e-03
-2023-11-09 08:47:26,174 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  3 -- Sweep:  1 -- residual: 1.40642621e-04
-2023-11-09 08:47:26,178 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  4 -- Sweep:  1 -- residual: 1.85982060e-05
-2023-11-09 08:47:26,182 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  5 -- Sweep:  1 -- residual: 2.79216661e-06
-2023-11-09 08:47:26,186 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  6 -- Sweep:  1 -- residual: 1.12278814e-06
-2023-11-09 08:47:26,190 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  7 -- Sweep:  1 -- residual: 2.85496359e-07
-2023-11-09 08:47:26,194 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  8 -- Sweep:  1 -- residual: 5.78932922e-08
-2023-11-09 08:47:26,198 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  9 -- Sweep:  1 -- residual: 9.68191199e-09
-2023-11-09 08:47:26,202 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration: 10 -- Sweep:  1 -- residual: 1.26386991e-09
-2023-11-09 08:47:26,206 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration: 11 -- Sweep:  1 -- residual: 1.83635938e-10
-2023-11-09 08:47:26,210 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration: 12 -- Sweep:  1 -- residual: 1.91962522e-11
-2023-11-09 08:47:26,211 - hooks - default_hook - post_run - 340 - INFO: Finished run after 0.10s
+2023-11-10 06:55:51,317 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  1 -- Sweep:  1 -- residual: 4.11190756e-03
+2023-11-10 06:55:51,321 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  2 -- Sweep:  1 -- residual: 6.68442665e-04
+2023-11-10 06:55:51,325 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  3 -- Sweep:  1 -- residual: 8.80377586e-05
+2023-11-10 06:55:51,329 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  4 -- Sweep:  1 -- residual: 1.21707912e-05
+2023-11-10 06:55:51,333 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  5 -- Sweep:  1 -- residual: 1.38272106e-06
+2023-11-10 06:55:51,337 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  6 -- Sweep:  1 -- residual: 6.36444759e-07
+2023-11-10 06:55:51,341 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  7 -- Sweep:  1 -- residual: 1.68953978e-07
+2023-11-10 06:55:51,345 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  8 -- Sweep:  1 -- residual: 3.52597535e-08
+2023-11-10 06:55:51,349 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  9 -- Sweep:  1 -- residual: 6.07222841e-09
+2023-11-10 06:55:51,353 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration: 10 -- Sweep:  1 -- residual: 8.28029601e-10
+2023-11-10 06:55:51,357 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration: 11 -- Sweep:  1 -- residual: 1.19626442e-10
+2023-11-10 06:55:51,361 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration: 12 -- Sweep:  1 -- residual: 1.44777350e-11
+2023-11-10 06:55:51,366 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  1 -- Sweep:  1 -- residual: 6.69984764e-03
+2023-11-10 06:55:51,370 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  2 -- Sweep:  1 -- residual: 1.05518433e-03
+2023-11-10 06:55:51,374 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  3 -- Sweep:  1 -- residual: 1.40642621e-04
+2023-11-10 06:55:51,378 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  4 -- Sweep:  1 -- residual: 1.85982060e-05
+2023-11-10 06:55:51,381 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  5 -- Sweep:  1 -- residual: 2.79216661e-06
+2023-11-10 06:55:51,385 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  6 -- Sweep:  1 -- residual: 1.12278814e-06
+2023-11-10 06:55:51,389 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  7 -- Sweep:  1 -- residual: 2.85496359e-07
+2023-11-10 06:55:51,393 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  8 -- Sweep:  1 -- residual: 5.78932922e-08
+2023-11-10 06:55:51,397 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  9 -- Sweep:  1 -- residual: 9.68191199e-09
+2023-11-10 06:55:51,401 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration: 10 -- Sweep:  1 -- residual: 1.26386991e-09
+2023-11-10 06:55:51,405 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration: 11 -- Sweep:  1 -- residual: 1.83635938e-10
+2023-11-10 06:55:51,409 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration: 12 -- Sweep:  1 -- residual: 1.91962522e-11
+2023-11-10 06:55:51,410 - hooks - default_hook - post_run - 340 - INFO: Finished run after 0.10s
 Error after SDC iterations: 1.166689e-05
 </pre></div>
 </div>
diff --git a/tutorial/doc_step_3_B.html b/tutorial/doc_step_3_B.html
index fbdd2185a6..ef2959223f 100644
--- a/tutorial/doc_step_3_B.html
+++ b/tutorial/doc_step_3_B.html
@@ -145,7 +145,7 @@ <h3>Navigation</h3>
 </pre></div>
 </div>
 <p>Results:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>2023-11-09 08:47:26,605 - controller - Controller - welcome_message - 146 - INFO: Welcome to the one and only, really very astonishing and 87.3% bug free
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>2023-11-10 06:55:51,797 - controller - Controller - welcome_message - 146 - INFO: Welcome to the one and only, really very astonishing and 87.3% bug free
                                  _____ _____   _____ 
                                 / ____|  __ \ / ____|
                     _ __  _   _| (___ | |  | | |     
@@ -155,8 +155,8 @@ <h3>Navigation</h3>
                    | |     __/ |                     
                    |_|    |___/                      
                                                      
-2023-11-09 08:47:26,606 - controller - Controller - dump_setup - 160 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- BEGIN
-2023-11-09 08:47:26,606 - controller - Controller - dump_setup - 227 - INFO: ----------------------------------------------------------------------------------------------------
+2023-11-10 06:55:51,797 - controller - Controller - dump_setup - 160 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- BEGIN
+2023-11-10 06:55:51,797 - controller - Controller - dump_setup - 227 - INFO: ----------------------------------------------------------------------------------------------------
 
 Controller: &lt;class &#39;pySDC.implementations.controller_classes.controller_nonMPI.controller_nonMPI&#39;&gt;
     all_to_done = False
@@ -204,21 +204,21 @@ <h3>Navigation</h3>
  -&gt; |  1 |   100 | SpreadStepSizesBlockwiseNonMPI
     |  2 |   200 | CheckConvergence
 
-2023-11-09 08:47:26,606 - controller - Controller - dump_setup - 230 - INFO: ----------------------------------------------------------------------------------------------------
-2023-11-09 08:47:26,606 - controller - Controller - dump_setup - 232 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- END
-
-2023-11-09 08:47:26,614 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  1 -- Sweep:  1 -- residual: 3.53203678e+00
-2023-11-09 08:47:26,620 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  2 -- Sweep:  1 -- residual: 2.09852117e-01
-2023-11-09 08:47:26,627 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  3 -- Sweep:  1 -- residual: 3.50301513e-02
-2023-11-09 08:47:26,634 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  4 -- Sweep:  1 -- residual: 4.67724741e-03
-2023-11-09 08:47:26,641 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  5 -- Sweep:  1 -- residual: 7.95583202e-04
-2023-11-09 08:47:26,648 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  6 -- Sweep:  1 -- residual: 1.11405073e-04
-2023-11-09 08:47:26,655 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  7 -- Sweep:  1 -- residual: 1.26902403e-05
-2023-11-09 08:47:26,662 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  8 -- Sweep:  1 -- residual: 1.16534547e-06
-2023-11-09 08:47:26,669 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  9 -- Sweep:  1 -- residual: 1.66968007e-07
-2023-11-09 08:47:26,675 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration: 10 -- Sweep:  1 -- residual: 2.09407887e-08
-2023-11-09 08:47:26,682 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration: 11 -- Sweep:  1 -- residual: 2.17123386e-09
-2023-11-09 08:47:26,685 - hooks - default_hook - post_run - 340 - INFO: Finished run after 0.08s
+2023-11-10 06:55:51,797 - controller - Controller - dump_setup - 230 - INFO: ----------------------------------------------------------------------------------------------------
+2023-11-10 06:55:51,797 - controller - Controller - dump_setup - 232 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- END
+
+2023-11-10 06:55:51,805 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  1 -- Sweep:  1 -- residual: 3.53203678e+00
+2023-11-10 06:55:51,812 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  2 -- Sweep:  1 -- residual: 2.09852117e-01
+2023-11-10 06:55:51,819 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  3 -- Sweep:  1 -- residual: 3.50301513e-02
+2023-11-10 06:55:51,826 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  4 -- Sweep:  1 -- residual: 4.67724741e-03
+2023-11-10 06:55:51,833 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  5 -- Sweep:  1 -- residual: 7.95583202e-04
+2023-11-10 06:55:51,840 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  6 -- Sweep:  1 -- residual: 1.11405073e-04
+2023-11-10 06:55:51,847 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  7 -- Sweep:  1 -- residual: 1.26902403e-05
+2023-11-10 06:55:51,854 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  8 -- Sweep:  1 -- residual: 1.16534547e-06
+2023-11-10 06:55:51,860 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  9 -- Sweep:  1 -- residual: 1.66968007e-07
+2023-11-10 06:55:51,867 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration: 10 -- Sweep:  1 -- residual: 2.09407887e-08
+2023-11-10 06:55:51,874 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration: 11 -- Sweep:  1 -- residual: 2.17123386e-09
+2023-11-10 06:55:51,877 - hooks - default_hook - post_run - 340 - INFO: Finished run after 0.08s
 Total energy and deviation in iteration  0: 8799.5000000000 -- 0.00000000e+00
 Total energy and deviation in iteration 11: 8785.0038936088 -- 1.44961064e+01
 </pre></div>
diff --git a/tutorial/doc_step_4_D.html b/tutorial/doc_step_4_D.html
index 9508b4ca88..64e96ab0e9 100644
--- a/tutorial/doc_step_4_D.html
+++ b/tutorial/doc_step_4_D.html
@@ -191,7 +191,7 @@ <h3>Navigation</h3>
 </pre></div>
 </div>
 <p>Results:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Timings</span> <span class="k">for</span> <span class="n">SDC</span><span class="p">,</span> <span class="n">MLSDC</span> <span class="ow">and</span> <span class="n">MLSDC</span><span class="o">+</span><span class="n">finter</span><span class="p">:</span>   <span class="mf">4.80360197</span> <span class="o">--</span>   <span class="mf">5.33965284</span> <span class="o">--</span>   <span class="mf">6.18355297</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Timings</span> <span class="k">for</span> <span class="n">SDC</span><span class="p">,</span> <span class="n">MLSDC</span> <span class="ow">and</span> <span class="n">MLSDC</span><span class="o">+</span><span class="n">finter</span><span class="p">:</span>   <span class="mf">4.80493993</span> <span class="o">--</span>   <span class="mf">5.37323094</span> <span class="o">--</span>   <span class="mf">6.18740526</span>
 <span class="n">Total</span> <span class="n">energy</span> <span class="ow">and</span> <span class="n">relative</span> <span class="n">deviation</span> <span class="ow">in</span> <span class="n">iteration</span>  <span class="mi">0</span><span class="p">:</span> <span class="mf">407936.7556966486</span> <span class="o">--</span> <span class="mf">0.00000000e+00</span>
 <span class="n">Total</span> <span class="n">energy</span> <span class="ow">and</span> <span class="n">relative</span> <span class="n">deviation</span> <span class="ow">in</span> <span class="n">iteration</span> <span class="mi">12</span><span class="p">:</span> <span class="mf">406977.9425667246</span> <span class="o">--</span> <span class="mf">2.35039652e-03</span>
 <span class="n">Total</span> <span class="n">energy</span> <span class="ow">and</span> <span class="n">relative</span> <span class="n">deviation</span> <span class="ow">in</span> <span class="n">iteration</span>  <span class="mi">0</span><span class="p">:</span> <span class="mf">407936.7556966486</span> <span class="o">--</span> <span class="mf">0.00000000e+00</span>
diff --git a/tutorial/doc_step_7_A.html b/tutorial/doc_step_7_A.html
index fc81d3217f..357b2ea961 100644
--- a/tutorial/doc_step_7_A.html
+++ b/tutorial/doc_step_7_A.html
@@ -223,49 +223,49 @@ <h3>Navigation</h3>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.6077</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.6125</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Variant</span> <span class="n">mass</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">False</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mi">1</span> <span class="o">--</span> <span class="n">error</span> <span class="n">at</span> <span class="n">time</span> <span class="mf">1.0</span><span class="p">:</span> <span class="mf">4.037998750179539e-08</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">6.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.2268</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.2183</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Variant</span> <span class="n">weak</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">False</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mi">1</span> <span class="o">--</span> <span class="n">error</span> <span class="n">at</span> <span class="n">time</span> <span class="mf">1.0</span><span class="p">:</span> <span class="mf">4.0388218372050104e-08</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">6.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">5.0355</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">4.9891</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Variant</span> <span class="n">mass_inv</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mi">1</span> <span class="o">--</span> <span class="n">error</span> <span class="n">at</span> <span class="n">time</span> <span class="mf">1.0</span><span class="p">:</span> <span class="mf">4.038030058561979e-08</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">6.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">2.2597</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">2.2539</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Variant</span> <span class="n">mass</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mi">1</span> <span class="o">--</span> <span class="n">error</span> <span class="n">at</span> <span class="n">time</span> <span class="mf">1.0</span><span class="p">:</span> <span class="mf">4.0380468789990663e-08</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">6.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.8499</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.8675</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Variant</span> <span class="n">weak</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mi">1</span> <span class="o">--</span> <span class="n">error</span> <span class="n">at</span> <span class="n">time</span> <span class="mf">1.0</span><span class="p">:</span> <span class="mf">4.038821713998089e-08</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">6.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.5567</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.4955</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Variant</span> <span class="n">mass_inv</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mi">5</span> <span class="o">--</span> <span class="n">error</span> <span class="n">at</span> <span class="n">time</span> <span class="mf">1.0</span><span class="p">:</span> <span class="mf">3.9537709137400506e-08</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">11.60</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">9</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">4</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">3.26</span> <span class="o">--</span> <span class="mf">10.64</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.6337</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.6622</span> <span class="n">sec</span><span class="o">.</span>
 
 </pre></div>
 </div>
diff --git a/tutorial/doc_step_7_B.html b/tutorial/doc_step_7_B.html
index bd4aa62753..c496b15c12 100644
--- a/tutorial/doc_step_7_B.html
+++ b/tutorial/doc_step_7_B.html
@@ -200,7 +200,7 @@ <h3>Navigation</h3>
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span> <span class="mi">19</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">2.10</span> <span class="o">--</span> <span class="mf">4.41</span>
 <span class="n">Error</span><span class="p">:</span> <span class="mf">1.1321e-05</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.3630</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.4876</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Running</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">False</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mf">1.</span><span class="o">..</span>
    <span class="n">Min</span><span class="o">/</span><span class="n">Mean</span><span class="o">/</span><span class="n">Max</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">8.00</span> <span class="o">/</span> <span class="mf">11.40</span> <span class="o">/</span> <span class="mf">15.00</span>
@@ -208,7 +208,7 @@ <h3>Navigation</h3>
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span> <span class="mi">19</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">2.03</span> <span class="o">--</span> <span class="mf">4.14</span>
 <span class="n">Error</span><span class="p">:</span> <span class="mf">4.1749e-06</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.0894</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">2.7871</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Running</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mf">1.</span><span class="o">..</span>
    <span class="n">Min</span><span class="o">/</span><span class="n">Mean</span><span class="o">/</span><span class="n">Max</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">5.00</span> <span class="o">/</span> <span class="mf">6.60</span> <span class="o">/</span> <span class="mf">8.00</span>
@@ -216,7 +216,7 @@ <h3>Navigation</h3>
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span> <span class="mi">16</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">1.07</span> <span class="o">--</span> <span class="mf">1.14</span>
 <span class="n">Error</span><span class="p">:</span> <span class="mf">1.1316e-05</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.3180</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.2984</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Running</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mf">1.</span><span class="o">..</span>
    <span class="n">Min</span><span class="o">/</span><span class="n">Mean</span><span class="o">/</span><span class="n">Max</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">4.00</span> <span class="o">/</span> <span class="mf">5.95</span> <span class="o">/</span> <span class="mf">8.00</span>
@@ -224,7 +224,7 @@ <h3>Navigation</h3>
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span> <span class="mi">19</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">1.02</span> <span class="o">--</span> <span class="mf">1.05</span>
 <span class="n">Error</span><span class="p">:</span> <span class="mf">4.1744e-06</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.2067</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.0261</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Running</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mf">10.</span><span class="o">..</span>
    <span class="n">Min</span><span class="o">/</span><span class="n">Mean</span><span class="o">/</span><span class="n">Max</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">7.00</span> <span class="o">/</span> <span class="mf">12.45</span> <span class="o">/</span> <span class="mf">18.00</span>
@@ -232,7 +232,7 @@ <h3>Navigation</h3>
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">9</span> <span class="o">--</span> <span class="mi">10</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">3.11</span> <span class="o">--</span> <span class="mf">9.65</span>
 <span class="n">Error</span><span class="p">:</span> <span class="mf">1.1306e-05</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">2.7432</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">6.8781</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Running</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mf">10.</span><span class="o">..</span>
    <span class="n">Min</span><span class="o">/</span><span class="n">Mean</span><span class="o">/</span><span class="n">Max</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">6.00</span> <span class="o">/</span> <span class="mf">11.50</span> <span class="o">/</span> <span class="mf">17.00</span>
@@ -240,7 +240,7 @@ <h3>Navigation</h3>
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">9</span> <span class="o">--</span> <span class="mi">10</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">3.04</span> <span class="o">--</span> <span class="mf">9.25</span>
 <span class="n">Error</span><span class="p">:</span> <span class="mf">4.1688e-06</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">2.5445</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">6.3209</span> <span class="n">sec</span><span class="o">.</span>
 
 </pre></div>
 </div>
diff --git a/tutorial/doc_step_7_C.html b/tutorial/doc_step_7_C.html
index bf9209dcd0..2ea97975db 100644
--- a/tutorial/doc_step_7_C.html
+++ b/tutorial/doc_step_7_C.html
@@ -215,7 +215,7 @@ <h3>Navigation</h3>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.9246</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.9039</span> <span class="n">sec</span><span class="o">.</span>
 <span class="n">Error</span> <span class="n">vs</span><span class="o">.</span> <span class="n">PDE</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.9479e-04</span>
 </pre></div>
 </div>
@@ -227,26 +227,26 @@ <h3>Navigation</h3>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">0.8496</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">0.8463</span> <span class="n">sec</span><span class="o">.</span>
 <span class="n">Error</span> <span class="n">vs</span><span class="o">.</span> <span class="n">PDE</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.9479e-04</span>
 </pre></div>
 </div>
 <p>2 processor in time, 2 processors in space</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">This</span> <span class="ow">is</span> <span class="n">time</span><span class="o">-</span><span class="n">rank</span> <span class="mf">0.</span><span class="o">..</span>
-<span class="n">Number</span> <span class="n">of</span> <span class="n">iterations</span> <span class="k">for</span> <span class="n">time</span> <span class="mf">0.00</span><span class="p">:</span> <span class="mi">12</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">This</span> <span class="ow">is</span> <span class="n">time</span><span class="o">-</span><span class="n">rank</span> <span class="mf">1.</span><span class="o">..</span>
+<span class="n">Number</span> <span class="n">of</span> <span class="n">iterations</span> <span class="k">for</span> <span class="n">time</span> <span class="mf">0.12</span><span class="p">:</span> <span class="mi">12</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">12.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">0.7566</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">0.7722</span> <span class="n">sec</span><span class="o">.</span>
 <span class="n">Error</span> <span class="n">vs</span><span class="o">.</span> <span class="n">PDE</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.9479e-04</span>
-<span class="n">This</span> <span class="ow">is</span> <span class="n">time</span><span class="o">-</span><span class="n">rank</span> <span class="mf">1.</span><span class="o">..</span>
-<span class="n">Number</span> <span class="n">of</span> <span class="n">iterations</span> <span class="k">for</span> <span class="n">time</span> <span class="mf">0.12</span><span class="p">:</span> <span class="mi">12</span>
+<span class="n">This</span> <span class="ow">is</span> <span class="n">time</span><span class="o">-</span><span class="n">rank</span> <span class="mf">0.</span><span class="o">..</span>
+<span class="n">Number</span> <span class="n">of</span> <span class="n">iterations</span> <span class="k">for</span> <span class="n">time</span> <span class="mf">0.00</span><span class="p">:</span> <span class="mi">12</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">12.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">0.7566</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">0.7731</span> <span class="n">sec</span><span class="o">.</span>
 <span class="n">Error</span> <span class="n">vs</span><span class="o">.</span> <span class="n">PDE</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.9479e-04</span>
 </pre></div>
 </div>
diff --git a/tutorial/doc_step_8_C.html b/tutorial/doc_step_8_C.html
index ceeb36f443..6d181cefa8 100644
--- a/tutorial/doc_step_8_C.html
+++ b/tutorial/doc_step_8_C.html
@@ -355,7 +355,7 @@ <h3>Navigation</h3>
    Errors after step   0.8750 with 6 iterations: 3.6530e-08 / 2.8821e-13
    Errors after step   1.0000 with 6 iterations: 3.6478e-08 / 1.8707e-13
 
-...done, took 0.4127275970001847 seconds!
+...done, took 0.4059683190000669 seconds!
 -----------------------------------------------------------------------------
 Running diffusion in 1 dimensions with time-step size 0.125...
 
@@ -369,7 +369,7 @@ <h3>Navigation</h3>
    Errors after step   0.8750 with 3 iterations: 3.5502e-08 / 2.1250e-13
    Errors after step   1.0000 with 3 iterations: 3.6813e-08 / 2.1660e-13
 
-...done, took 0.9221518619999642 seconds!
+...done, took 0.9272980149999057 seconds!
 -----------------------------------------------------------------------------
 Running advection in 1 dimensions with time-step size 0.125...
 
@@ -383,7 +383,7 @@ <h3>Navigation</h3>
    Errors after step   0.8750 with 4 iterations: 2.5517e-08 / 7.7716e-16
    Errors after step   1.0000 with 4 iterations: 2.9147e-08 / 5.5511e-16
 
-...done, took 0.25231512099981046 seconds!
+...done, took 0.25329556399992725 seconds!
 -----------------------------------------------------------------------------
 Running advection in 1 dimensions with time-step size 0.125...
 
@@ -397,7 +397,7 @@ <h3>Navigation</h3>
    Errors after step   0.8750 with 2 iterations: 2.5987e-08 / 3.1841e-13
    Errors after step   1.0000 with 2 iterations: 2.9666e-08 / 3.1808e-13
 
-...done, took 0.7320644420001372 seconds!
+...done, took 0.7298739230000137 seconds!
 -----------------------------------------------------------------------------
 Running auzinger in 1 dimensions with time-step size 0.125...
 
@@ -411,7 +411,7 @@ <h3>Navigation</h3>
    Errors after step   0.8750 with 6 iterations: 2.8266e-08 / 0.0000e+00
    Errors after step   1.0000 with 6 iterations: 2.8338e-08 / 0.0000e+00
 
-...done, took 0.17040672499979337 seconds!
+...done, took 0.17030540900009328 seconds!
 -----------------------------------------------------------------------------
 Running auzinger in 1 dimensions with time-step size 0.125...
 
@@ -425,7 +425,7 @@ <h3>Navigation</h3>
    Errors after step   0.8750 with 4 iterations: 3.1486e-08 / 0.0000e+00
    Errors after step   1.0000 with 4 iterations: 3.3802e-08 / 0.0000e+00
 
-...done, took 0.20881961100008084 seconds!
+...done, took 0.20317804299997988 seconds!
 -----------------------------------------------------------------------------
 </pre></div>
 </div>
diff --git a/tutorial/step_2.html b/tutorial/step_2.html
index 1d643ac8fd..0a660e0f12 100644
--- a/tutorial/step_2.html
+++ b/tutorial/step_2.html
@@ -417,7 +417,7 @@ <h2>Part C: Using pySDC’s frontend<a class="headerlink" href="#part-c-using-py
 </pre></div>
 </div>
 <p>Results:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>2023-11-09 08:47:26,112 - controller - Controller - welcome_message - 146 - INFO: Welcome to the one and only, really very astonishing and 87.3% bug free
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>2023-11-10 06:55:51,312 - controller - Controller - welcome_message - 146 - INFO: Welcome to the one and only, really very astonishing and 87.3% bug free
                                  _____ _____   _____ 
                                 / ____|  __ \ / ____|
                     _ __  _   _| (___ | |  | | |     
@@ -427,8 +427,8 @@ <h2>Part C: Using pySDC’s frontend<a class="headerlink" href="#part-c-using-py
                    | |     __/ |                     
                    |_|    |___/                      
                                                      
-2023-11-09 08:47:26,112 - controller - Controller - dump_setup - 160 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- BEGIN
-2023-11-09 08:47:26,113 - controller - Controller - dump_setup - 227 - INFO: ----------------------------------------------------------------------------------------------------
+2023-11-10 06:55:51,312 - controller - Controller - dump_setup - 160 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- BEGIN
+2023-11-10 06:55:51,313 - controller - Controller - dump_setup - 227 - INFO: ----------------------------------------------------------------------------------------------------
 
 Controller: &lt;class &#39;pySDC.implementations.controller_classes.controller_nonMPI.controller_nonMPI&#39;&gt;
     all_to_done = False
@@ -481,34 +481,34 @@ <h2>Part C: Using pySDC’s frontend<a class="headerlink" href="#part-c-using-py
  -&gt; |  1 |   100 | SpreadStepSizesBlockwiseNonMPI
     |  2 |   200 | CheckConvergence
 
-2023-11-09 08:47:26,113 - controller - Controller - dump_setup - 230 - INFO: ----------------------------------------------------------------------------------------------------
-2023-11-09 08:47:26,113 - controller - Controller - dump_setup - 232 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- END
-
-2023-11-09 08:47:26,117 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  1 -- Sweep:  1 -- residual: 4.11190756e-03
-2023-11-09 08:47:26,121 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  2 -- Sweep:  1 -- residual: 6.68442665e-04
-2023-11-09 08:47:26,125 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  3 -- Sweep:  1 -- residual: 8.80377586e-05
-2023-11-09 08:47:26,129 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  4 -- Sweep:  1 -- residual: 1.21707912e-05
-2023-11-09 08:47:26,133 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  5 -- Sweep:  1 -- residual: 1.38272106e-06
-2023-11-09 08:47:26,137 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  6 -- Sweep:  1 -- residual: 6.36444759e-07
-2023-11-09 08:47:26,141 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  7 -- Sweep:  1 -- residual: 1.68953978e-07
-2023-11-09 08:47:26,145 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  8 -- Sweep:  1 -- residual: 3.52597535e-08
-2023-11-09 08:47:26,149 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  9 -- Sweep:  1 -- residual: 6.07222841e-09
-2023-11-09 08:47:26,153 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration: 10 -- Sweep:  1 -- residual: 8.28029601e-10
-2023-11-09 08:47:26,157 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration: 11 -- Sweep:  1 -- residual: 1.19626442e-10
-2023-11-09 08:47:26,161 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration: 12 -- Sweep:  1 -- residual: 1.44777350e-11
-2023-11-09 08:47:26,166 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  1 -- Sweep:  1 -- residual: 6.69984764e-03
-2023-11-09 08:47:26,170 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  2 -- Sweep:  1 -- residual: 1.05518433e-03
-2023-11-09 08:47:26,174 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  3 -- Sweep:  1 -- residual: 1.40642621e-04
-2023-11-09 08:47:26,178 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  4 -- Sweep:  1 -- residual: 1.85982060e-05
-2023-11-09 08:47:26,182 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  5 -- Sweep:  1 -- residual: 2.79216661e-06
-2023-11-09 08:47:26,186 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  6 -- Sweep:  1 -- residual: 1.12278814e-06
-2023-11-09 08:47:26,190 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  7 -- Sweep:  1 -- residual: 2.85496359e-07
-2023-11-09 08:47:26,194 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  8 -- Sweep:  1 -- residual: 5.78932922e-08
-2023-11-09 08:47:26,198 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  9 -- Sweep:  1 -- residual: 9.68191199e-09
-2023-11-09 08:47:26,202 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration: 10 -- Sweep:  1 -- residual: 1.26386991e-09
-2023-11-09 08:47:26,206 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration: 11 -- Sweep:  1 -- residual: 1.83635938e-10
-2023-11-09 08:47:26,210 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration: 12 -- Sweep:  1 -- residual: 1.91962522e-11
-2023-11-09 08:47:26,211 - hooks - default_hook - post_run - 340 - INFO: Finished run after 0.10s
+2023-11-10 06:55:51,313 - controller - Controller - dump_setup - 230 - INFO: ----------------------------------------------------------------------------------------------------
+2023-11-10 06:55:51,313 - controller - Controller - dump_setup - 232 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- END
+
+2023-11-10 06:55:51,317 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  1 -- Sweep:  1 -- residual: 4.11190756e-03
+2023-11-10 06:55:51,321 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  2 -- Sweep:  1 -- residual: 6.68442665e-04
+2023-11-10 06:55:51,325 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  3 -- Sweep:  1 -- residual: 8.80377586e-05
+2023-11-10 06:55:51,329 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  4 -- Sweep:  1 -- residual: 1.21707912e-05
+2023-11-10 06:55:51,333 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  5 -- Sweep:  1 -- residual: 1.38272106e-06
+2023-11-10 06:55:51,337 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  6 -- Sweep:  1 -- residual: 6.36444759e-07
+2023-11-10 06:55:51,341 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  7 -- Sweep:  1 -- residual: 1.68953978e-07
+2023-11-10 06:55:51,345 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  8 -- Sweep:  1 -- residual: 3.52597535e-08
+2023-11-10 06:55:51,349 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration:  9 -- Sweep:  1 -- residual: 6.07222841e-09
+2023-11-10 06:55:51,353 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration: 10 -- Sweep:  1 -- residual: 8.28029601e-10
+2023-11-10 06:55:51,357 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration: 11 -- Sweep:  1 -- residual: 1.19626442e-10
+2023-11-10 06:55:51,361 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.100000 at stage         IT_FINE: Level: 0 -- Iteration: 12 -- Sweep:  1 -- residual: 1.44777350e-11
+2023-11-10 06:55:51,366 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  1 -- Sweep:  1 -- residual: 6.69984764e-03
+2023-11-10 06:55:51,370 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  2 -- Sweep:  1 -- residual: 1.05518433e-03
+2023-11-10 06:55:51,374 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  3 -- Sweep:  1 -- residual: 1.40642621e-04
+2023-11-10 06:55:51,378 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  4 -- Sweep:  1 -- residual: 1.85982060e-05
+2023-11-10 06:55:51,381 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  5 -- Sweep:  1 -- residual: 2.79216661e-06
+2023-11-10 06:55:51,385 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  6 -- Sweep:  1 -- residual: 1.12278814e-06
+2023-11-10 06:55:51,389 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  7 -- Sweep:  1 -- residual: 2.85496359e-07
+2023-11-10 06:55:51,393 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  8 -- Sweep:  1 -- residual: 5.78932922e-08
+2023-11-10 06:55:51,397 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration:  9 -- Sweep:  1 -- residual: 9.68191199e-09
+2023-11-10 06:55:51,401 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration: 10 -- Sweep:  1 -- residual: 1.26386991e-09
+2023-11-10 06:55:51,405 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration: 11 -- Sweep:  1 -- residual: 1.83635938e-10
+2023-11-10 06:55:51,409 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.200000 at stage         IT_FINE: Level: 0 -- Iteration: 12 -- Sweep:  1 -- residual: 1.91962522e-11
+2023-11-10 06:55:51,410 - hooks - default_hook - post_run - 340 - INFO: Finished run after 0.10s
 Error after SDC iterations: 1.166689e-05
 </pre></div>
 </div>
diff --git a/tutorial/step_3.html b/tutorial/step_3.html
index 01dc9605d1..99ce6547bc 100644
--- a/tutorial/step_3.html
+++ b/tutorial/step_3.html
@@ -344,7 +344,7 @@ <h2>Part B: Adding statistics<a class="headerlink" href="#part-b-adding-statisti
 </pre></div>
 </div>
 <p>Results:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>2023-11-09 08:47:26,605 - controller - Controller - welcome_message - 146 - INFO: Welcome to the one and only, really very astonishing and 87.3% bug free
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>2023-11-10 06:55:51,797 - controller - Controller - welcome_message - 146 - INFO: Welcome to the one and only, really very astonishing and 87.3% bug free
                                  _____ _____   _____ 
                                 / ____|  __ \ / ____|
                     _ __  _   _| (___ | |  | | |     
@@ -354,8 +354,8 @@ <h2>Part B: Adding statistics<a class="headerlink" href="#part-b-adding-statisti
                    | |     __/ |                     
                    |_|    |___/                      
                                                      
-2023-11-09 08:47:26,606 - controller - Controller - dump_setup - 160 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- BEGIN
-2023-11-09 08:47:26,606 - controller - Controller - dump_setup - 227 - INFO: ----------------------------------------------------------------------------------------------------
+2023-11-10 06:55:51,797 - controller - Controller - dump_setup - 160 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- BEGIN
+2023-11-10 06:55:51,797 - controller - Controller - dump_setup - 227 - INFO: ----------------------------------------------------------------------------------------------------
 
 Controller: &lt;class &#39;pySDC.implementations.controller_classes.controller_nonMPI.controller_nonMPI&#39;&gt;
     all_to_done = False
@@ -403,21 +403,21 @@ <h2>Part B: Adding statistics<a class="headerlink" href="#part-b-adding-statisti
  -&gt; |  1 |   100 | SpreadStepSizesBlockwiseNonMPI
     |  2 |   200 | CheckConvergence
 
-2023-11-09 08:47:26,606 - controller - Controller - dump_setup - 230 - INFO: ----------------------------------------------------------------------------------------------------
-2023-11-09 08:47:26,606 - controller - Controller - dump_setup - 232 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- END
-
-2023-11-09 08:47:26,614 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  1 -- Sweep:  1 -- residual: 3.53203678e+00
-2023-11-09 08:47:26,620 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  2 -- Sweep:  1 -- residual: 2.09852117e-01
-2023-11-09 08:47:26,627 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  3 -- Sweep:  1 -- residual: 3.50301513e-02
-2023-11-09 08:47:26,634 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  4 -- Sweep:  1 -- residual: 4.67724741e-03
-2023-11-09 08:47:26,641 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  5 -- Sweep:  1 -- residual: 7.95583202e-04
-2023-11-09 08:47:26,648 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  6 -- Sweep:  1 -- residual: 1.11405073e-04
-2023-11-09 08:47:26,655 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  7 -- Sweep:  1 -- residual: 1.26902403e-05
-2023-11-09 08:47:26,662 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  8 -- Sweep:  1 -- residual: 1.16534547e-06
-2023-11-09 08:47:26,669 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  9 -- Sweep:  1 -- residual: 1.66968007e-07
-2023-11-09 08:47:26,675 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration: 10 -- Sweep:  1 -- residual: 2.09407887e-08
-2023-11-09 08:47:26,682 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration: 11 -- Sweep:  1 -- residual: 2.17123386e-09
-2023-11-09 08:47:26,685 - hooks - default_hook - post_run - 340 - INFO: Finished run after 0.08s
+2023-11-10 06:55:51,797 - controller - Controller - dump_setup - 230 - INFO: ----------------------------------------------------------------------------------------------------
+2023-11-10 06:55:51,797 - controller - Controller - dump_setup - 232 - INFO: Setup overview (--&gt; user-defined, -&gt; dependency) -- END
+
+2023-11-10 06:55:51,805 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  1 -- Sweep:  1 -- residual: 3.53203678e+00
+2023-11-10 06:55:51,812 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  2 -- Sweep:  1 -- residual: 2.09852117e-01
+2023-11-10 06:55:51,819 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  3 -- Sweep:  1 -- residual: 3.50301513e-02
+2023-11-10 06:55:51,826 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  4 -- Sweep:  1 -- residual: 4.67724741e-03
+2023-11-10 06:55:51,833 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  5 -- Sweep:  1 -- residual: 7.95583202e-04
+2023-11-10 06:55:51,840 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  6 -- Sweep:  1 -- residual: 1.11405073e-04
+2023-11-10 06:55:51,847 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  7 -- Sweep:  1 -- residual: 1.26902403e-05
+2023-11-10 06:55:51,854 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  8 -- Sweep:  1 -- residual: 1.16534547e-06
+2023-11-10 06:55:51,860 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration:  9 -- Sweep:  1 -- residual: 1.66968007e-07
+2023-11-10 06:55:51,867 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration: 10 -- Sweep:  1 -- residual: 2.09407887e-08
+2023-11-10 06:55:51,874 - hooks - default_hook - post_sweep - 170 - INFO: Process  0 on time 0.000000 at stage         IT_FINE: Level: 0 -- Iteration: 11 -- Sweep:  1 -- residual: 2.17123386e-09
+2023-11-10 06:55:51,877 - hooks - default_hook - post_run - 340 - INFO: Finished run after 0.08s
 Total energy and deviation in iteration  0: 8799.5000000000 -- 0.00000000e+00
 Total energy and deviation in iteration 11: 8785.0038936088 -- 1.44961064e+01
 </pre></div>
diff --git a/tutorial/step_4.html b/tutorial/step_4.html
index c0443a5b64..6bb1a9fb04 100644
--- a/tutorial/step_4.html
+++ b/tutorial/step_4.html
@@ -619,7 +619,7 @@ <h2>Part D: MLSDC with particles<a class="headerlink" href="#part-d-mlsdc-with-p
 </pre></div>
 </div>
 <p>Results:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Timings</span> <span class="k">for</span> <span class="n">SDC</span><span class="p">,</span> <span class="n">MLSDC</span> <span class="ow">and</span> <span class="n">MLSDC</span><span class="o">+</span><span class="n">finter</span><span class="p">:</span>   <span class="mf">4.80360197</span> <span class="o">--</span>   <span class="mf">5.33965284</span> <span class="o">--</span>   <span class="mf">6.18355297</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Timings</span> <span class="k">for</span> <span class="n">SDC</span><span class="p">,</span> <span class="n">MLSDC</span> <span class="ow">and</span> <span class="n">MLSDC</span><span class="o">+</span><span class="n">finter</span><span class="p">:</span>   <span class="mf">4.80493993</span> <span class="o">--</span>   <span class="mf">5.37323094</span> <span class="o">--</span>   <span class="mf">6.18740526</span>
 <span class="n">Total</span> <span class="n">energy</span> <span class="ow">and</span> <span class="n">relative</span> <span class="n">deviation</span> <span class="ow">in</span> <span class="n">iteration</span>  <span class="mi">0</span><span class="p">:</span> <span class="mf">407936.7556966486</span> <span class="o">--</span> <span class="mf">0.00000000e+00</span>
 <span class="n">Total</span> <span class="n">energy</span> <span class="ow">and</span> <span class="n">relative</span> <span class="n">deviation</span> <span class="ow">in</span> <span class="n">iteration</span> <span class="mi">12</span><span class="p">:</span> <span class="mf">406977.9425667246</span> <span class="o">--</span> <span class="mf">2.35039652e-03</span>
 <span class="n">Total</span> <span class="n">energy</span> <span class="ow">and</span> <span class="n">relative</span> <span class="n">deviation</span> <span class="ow">in</span> <span class="n">iteration</span>  <span class="mi">0</span><span class="p">:</span> <span class="mf">407936.7556966486</span> <span class="o">--</span> <span class="mf">0.00000000e+00</span>
diff --git a/tutorial/step_7.html b/tutorial/step_7.html
index 1987ccbe57..ff5d40f86b 100644
--- a/tutorial/step_7.html
+++ b/tutorial/step_7.html
@@ -247,49 +247,49 @@ <h2>Part A: pySDC and FEniCS<a class="headerlink" href="#part-a-pysdc-and-fenics
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.6077</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.6125</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Variant</span> <span class="n">mass</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">False</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mi">1</span> <span class="o">--</span> <span class="n">error</span> <span class="n">at</span> <span class="n">time</span> <span class="mf">1.0</span><span class="p">:</span> <span class="mf">4.037998750179539e-08</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">6.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.2268</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.2183</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Variant</span> <span class="n">weak</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">False</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mi">1</span> <span class="o">--</span> <span class="n">error</span> <span class="n">at</span> <span class="n">time</span> <span class="mf">1.0</span><span class="p">:</span> <span class="mf">4.0388218372050104e-08</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">6.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">5.0355</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">4.9891</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Variant</span> <span class="n">mass_inv</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mi">1</span> <span class="o">--</span> <span class="n">error</span> <span class="n">at</span> <span class="n">time</span> <span class="mf">1.0</span><span class="p">:</span> <span class="mf">4.038030058561979e-08</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">6.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">2.2597</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">2.2539</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Variant</span> <span class="n">mass</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mi">1</span> <span class="o">--</span> <span class="n">error</span> <span class="n">at</span> <span class="n">time</span> <span class="mf">1.0</span><span class="p">:</span> <span class="mf">4.0380468789990663e-08</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">6.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.8499</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.8675</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Variant</span> <span class="n">weak</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mi">1</span> <span class="o">--</span> <span class="n">error</span> <span class="n">at</span> <span class="n">time</span> <span class="mf">1.0</span><span class="p">:</span> <span class="mf">4.038821713998089e-08</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">6.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.5567</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.4955</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Variant</span> <span class="n">mass_inv</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mi">5</span> <span class="o">--</span> <span class="n">error</span> <span class="n">at</span> <span class="n">time</span> <span class="mf">1.0</span><span class="p">:</span> <span class="mf">3.9537709137400506e-08</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">11.60</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">9</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">4</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">3.26</span> <span class="o">--</span> <span class="mf">10.64</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.6337</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.6622</span> <span class="n">sec</span><span class="o">.</span>
 
 </pre></div>
 </div>
@@ -470,7 +470,7 @@ <h2>Part B: mpi4py-fft for parallel Fourier transforms<a class="headerlink" href
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span> <span class="mi">19</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">2.10</span> <span class="o">--</span> <span class="mf">4.41</span>
 <span class="n">Error</span><span class="p">:</span> <span class="mf">1.1321e-05</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.3630</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.4876</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Running</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">False</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mf">1.</span><span class="o">..</span>
    <span class="n">Min</span><span class="o">/</span><span class="n">Mean</span><span class="o">/</span><span class="n">Max</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">8.00</span> <span class="o">/</span> <span class="mf">11.40</span> <span class="o">/</span> <span class="mf">15.00</span>
@@ -478,7 +478,7 @@ <h2>Part B: mpi4py-fft for parallel Fourier transforms<a class="headerlink" href
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span> <span class="mi">19</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">2.03</span> <span class="o">--</span> <span class="mf">4.14</span>
 <span class="n">Error</span><span class="p">:</span> <span class="mf">4.1749e-06</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.0894</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">2.7871</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Running</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mf">1.</span><span class="o">..</span>
    <span class="n">Min</span><span class="o">/</span><span class="n">Mean</span><span class="o">/</span><span class="n">Max</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">5.00</span> <span class="o">/</span> <span class="mf">6.60</span> <span class="o">/</span> <span class="mf">8.00</span>
@@ -486,7 +486,7 @@ <h2>Part B: mpi4py-fft for parallel Fourier transforms<a class="headerlink" href
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span> <span class="mi">16</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">1.07</span> <span class="o">--</span> <span class="mf">1.14</span>
 <span class="n">Error</span><span class="p">:</span> <span class="mf">1.1316e-05</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.3180</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.2984</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Running</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mf">1.</span><span class="o">..</span>
    <span class="n">Min</span><span class="o">/</span><span class="n">Mean</span><span class="o">/</span><span class="n">Max</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">4.00</span> <span class="o">/</span> <span class="mf">5.95</span> <span class="o">/</span> <span class="mf">8.00</span>
@@ -494,7 +494,7 @@ <h2>Part B: mpi4py-fft for parallel Fourier transforms<a class="headerlink" href
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span> <span class="mi">19</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">1.02</span> <span class="o">--</span> <span class="mf">1.05</span>
 <span class="n">Error</span><span class="p">:</span> <span class="mf">4.1744e-06</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.2067</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">3.0261</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Running</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mf">10.</span><span class="o">..</span>
    <span class="n">Min</span><span class="o">/</span><span class="n">Mean</span><span class="o">/</span><span class="n">Max</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">7.00</span> <span class="o">/</span> <span class="mf">12.45</span> <span class="o">/</span> <span class="mf">18.00</span>
@@ -502,7 +502,7 @@ <h2>Part B: mpi4py-fft for parallel Fourier transforms<a class="headerlink" href
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">9</span> <span class="o">--</span> <span class="mi">10</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">3.11</span> <span class="o">--</span> <span class="mf">9.65</span>
 <span class="n">Error</span><span class="p">:</span> <span class="mf">1.1306e-05</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">2.7432</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">6.8781</span> <span class="n">sec</span><span class="o">.</span>
 
 <span class="n">Running</span> <span class="k">with</span> <span class="n">ml</span><span class="o">=</span><span class="kc">True</span> <span class="ow">and</span> <span class="n">num_procs</span><span class="o">=</span><span class="mf">10.</span><span class="o">..</span>
    <span class="n">Min</span><span class="o">/</span><span class="n">Mean</span><span class="o">/</span><span class="n">Max</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">6.00</span> <span class="o">/</span> <span class="mf">11.50</span> <span class="o">/</span> <span class="mf">17.00</span>
@@ -510,7 +510,7 @@ <h2>Part B: mpi4py-fft for parallel Fourier transforms<a class="headerlink" href
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">9</span> <span class="o">--</span> <span class="mi">10</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">3.04</span> <span class="o">--</span> <span class="mf">9.25</span>
 <span class="n">Error</span><span class="p">:</span> <span class="mf">4.1688e-06</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">2.5445</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">6.3209</span> <span class="n">sec</span><span class="o">.</span>
 
 </pre></div>
 </div>
@@ -705,7 +705,7 @@ <h2>Part C: Time-parallel pySDC with space-parallel PETSc<a class="headerlink" h
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.9246</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.9039</span> <span class="n">sec</span><span class="o">.</span>
 <span class="n">Error</span> <span class="n">vs</span><span class="o">.</span> <span class="n">PDE</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.9479e-04</span>
 </pre></div>
 </div>
@@ -717,26 +717,26 @@ <h2>Part C: Time-parallel pySDC with space-parallel PETSc<a class="headerlink" h
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">0.8496</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">0.8463</span> <span class="n">sec</span><span class="o">.</span>
 <span class="n">Error</span> <span class="n">vs</span><span class="o">.</span> <span class="n">PDE</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.9479e-04</span>
 </pre></div>
 </div>
 <p>2 processor in time, 2 processors in space</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">This</span> <span class="ow">is</span> <span class="n">time</span><span class="o">-</span><span class="n">rank</span> <span class="mf">0.</span><span class="o">..</span>
-<span class="n">Number</span> <span class="n">of</span> <span class="n">iterations</span> <span class="k">for</span> <span class="n">time</span> <span class="mf">0.00</span><span class="p">:</span> <span class="mi">12</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">This</span> <span class="ow">is</span> <span class="n">time</span><span class="o">-</span><span class="n">rank</span> <span class="mf">1.</span><span class="o">..</span>
+<span class="n">Number</span> <span class="n">of</span> <span class="n">iterations</span> <span class="k">for</span> <span class="n">time</span> <span class="mf">0.12</span><span class="p">:</span> <span class="mi">12</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">12.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">0.7566</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">0.7722</span> <span class="n">sec</span><span class="o">.</span>
 <span class="n">Error</span> <span class="n">vs</span><span class="o">.</span> <span class="n">PDE</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.9479e-04</span>
-<span class="n">This</span> <span class="ow">is</span> <span class="n">time</span><span class="o">-</span><span class="n">rank</span> <span class="mf">1.</span><span class="o">..</span>
-<span class="n">Number</span> <span class="n">of</span> <span class="n">iterations</span> <span class="k">for</span> <span class="n">time</span> <span class="mf">0.12</span><span class="p">:</span> <span class="mi">12</span>
+<span class="n">This</span> <span class="ow">is</span> <span class="n">time</span><span class="o">-</span><span class="n">rank</span> <span class="mf">0.</span><span class="o">..</span>
+<span class="n">Number</span> <span class="n">of</span> <span class="n">iterations</span> <span class="k">for</span> <span class="n">time</span> <span class="mf">0.00</span><span class="p">:</span> <span class="mi">12</span>
    <span class="n">Mean</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">12.00</span>
    <span class="n">Range</span> <span class="n">of</span> <span class="n">values</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> 
    <span class="n">Position</span> <span class="n">of</span> <span class="nb">max</span><span class="o">/</span><span class="nb">min</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span>  <span class="mi">0</span> <span class="o">--</span>  <span class="mi">0</span>
    <span class="n">Std</span> <span class="ow">and</span> <span class="n">var</span> <span class="k">for</span> <span class="n">number</span> <span class="n">of</span> <span class="n">iterations</span><span class="p">:</span> <span class="mf">0.00</span> <span class="o">--</span> <span class="mf">0.00</span>
-<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">0.7566</span> <span class="n">sec</span><span class="o">.</span>
+<span class="n">Time</span> <span class="n">to</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">0.7731</span> <span class="n">sec</span><span class="o">.</span>
 <span class="n">Error</span> <span class="n">vs</span><span class="o">.</span> <span class="n">PDE</span> <span class="n">solution</span><span class="p">:</span> <span class="mf">1.9479e-04</span>
 </pre></div>
 </div>
diff --git a/tutorial/step_8.html b/tutorial/step_8.html
index d9572e2a2b..43554d55c5 100644
--- a/tutorial/step_8.html
+++ b/tutorial/step_8.html
@@ -675,7 +675,7 @@ <h2>Part C: Iteration estimator<a class="headerlink" href="#part-c-iteration-est
    Errors after step   0.8750 with 6 iterations: 3.6530e-08 / 2.8821e-13
    Errors after step   1.0000 with 6 iterations: 3.6478e-08 / 1.8707e-13
 
-...done, took 0.4127275970001847 seconds!
+...done, took 0.4059683190000669 seconds!
 -----------------------------------------------------------------------------
 Running diffusion in 1 dimensions with time-step size 0.125...
 
@@ -689,7 +689,7 @@ <h2>Part C: Iteration estimator<a class="headerlink" href="#part-c-iteration-est
    Errors after step   0.8750 with 3 iterations: 3.5502e-08 / 2.1250e-13
    Errors after step   1.0000 with 3 iterations: 3.6813e-08 / 2.1660e-13
 
-...done, took 0.9221518619999642 seconds!
+...done, took 0.9272980149999057 seconds!
 -----------------------------------------------------------------------------
 Running advection in 1 dimensions with time-step size 0.125...
 
@@ -703,7 +703,7 @@ <h2>Part C: Iteration estimator<a class="headerlink" href="#part-c-iteration-est
    Errors after step   0.8750 with 4 iterations: 2.5517e-08 / 7.7716e-16
    Errors after step   1.0000 with 4 iterations: 2.9147e-08 / 5.5511e-16
 
-...done, took 0.25231512099981046 seconds!
+...done, took 0.25329556399992725 seconds!
 -----------------------------------------------------------------------------
 Running advection in 1 dimensions with time-step size 0.125...
 
@@ -717,7 +717,7 @@ <h2>Part C: Iteration estimator<a class="headerlink" href="#part-c-iteration-est
    Errors after step   0.8750 with 2 iterations: 2.5987e-08 / 3.1841e-13
    Errors after step   1.0000 with 2 iterations: 2.9666e-08 / 3.1808e-13
 
-...done, took 0.7320644420001372 seconds!
+...done, took 0.7298739230000137 seconds!
 -----------------------------------------------------------------------------
 Running auzinger in 1 dimensions with time-step size 0.125...
 
@@ -731,7 +731,7 @@ <h2>Part C: Iteration estimator<a class="headerlink" href="#part-c-iteration-est
    Errors after step   0.8750 with 6 iterations: 2.8266e-08 / 0.0000e+00
    Errors after step   1.0000 with 6 iterations: 2.8338e-08 / 0.0000e+00
 
-...done, took 0.17040672499979337 seconds!
+...done, took 0.17030540900009328 seconds!
 -----------------------------------------------------------------------------
 Running auzinger in 1 dimensions with time-step size 0.125...
 
@@ -745,7 +745,7 @@ <h2>Part C: Iteration estimator<a class="headerlink" href="#part-c-iteration-est
    Errors after step   0.8750 with 4 iterations: 3.1486e-08 / 0.0000e+00
    Errors after step   1.0000 with 4 iterations: 3.3802e-08 / 0.0000e+00
 
-...done, took 0.20881961100008084 seconds!
+...done, took 0.20317804299997988 seconds!
 -----------------------------------------------------------------------------
 </pre></div>
 </div>