Updating documentation

find_edge_connectivity.m

@@ -1,5 +1,5 @@
 function [t_ed] = find_edge_connectivity(t,ed,mesh)
-% FIND_EDGES - Find the edges in each triangulation in the mesh
+% FIND_EDGE_CONNECTIVITY - Find the edges in each triangulation in the mesh
 %
 % Syntax:
 %     [ed, t_ed] = find_edges(t)
@@ -20,7 +20,9 @@
 % Date: Fall 2020
 
 if exist('mesh','var')
-	% mesh is given
+	% if mesh is given
+    % determine if we have saved a matrix for the given mesh & domain to
+    % save computational time
     if mesh == 6 && isfile('edge_resources/t_ed_6.mat')
         t_ed_6 = load('edge_resources/t_ed_6.mat');
         t_ed = t_ed_6.t_ed_6;

k_0/data/get_data1.m

@@ -4,6 +4,8 @@
 %   data1
 %   u = (1/3)r^3 - (1/2)r^2
 %   f = -(8/3)r + (5/2)
+% Author: Nicole Stock
+% Date: Fall 2020
 
 f = @(r,z) -(8./3).*r + (3./2);
 grad_f_r =@(r,z) -8./3;

k_0/data/get_data2.m

@@ -4,6 +4,8 @@
 %   data2
 %   u = r^3 - (3/2)r^2
 %   f = -8r + 9/2
+% Author: Nicole Stock
+% Date: Fall 2020
 
 f = @(r,z) -8.*r + (9./2);
 grad_f_r =@(r,z) -8;

k_0/data/get_data3.m

@@ -2,6 +2,8 @@
 %GET_U_DATA3 Get u and f function handles
 %
 %   u = r^(1/2)
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u = @(r,z) r.^(1./2);
 grad_u_r =@(r,z) (1./2).*r.^(-1./2);

k_0/data/get_data4.m

@@ -2,6 +2,8 @@
 %GET_U_DATA4 Get u and f function handles
 %
 %   u = r^(2/3)
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u = @(r,z) r.^(2./3);
 grad_u_r =@(r,z) (2./3).*r.^(-1./3);

k_0/data/get_data5.m

@@ -2,6 +2,8 @@
 %GET_U_DATA5 Get u and f function handles
 %
 %   u = r^(5/6)
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u = @(r,z) r.^(5./6);
 grad_u_r =@(r,z) (5./6).*r.^(-1./6);

k_0/data/get_data6.m

@@ -2,6 +2,8 @@
 %GET_U_DATA6 Get u and f function handles
 %
 %   u = r*sin(z)
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u = @(r,z) r.*sin(z);
 grad_u_r =@(r,z) sin(z);

k_0/data/get_data7.m

@@ -2,6 +2,8 @@
 %GET_U_DATA7 Get u and f function handles
 %
 %   u = r^(1/3)
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u = @(r,z) r.^(1./3);
 grad_u_r =@(r,z) (1./3).*r.^(-2./3);

k_0/data/get_data8.m

@@ -2,6 +2,8 @@
 %GET_U_DATA8 Get u and f function handles
 %   data3
 %   u = r^(4/3)
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u = @(r,z) r.^(4./3);
 grad_u_r =@(r,z) (4./3).*r.^(1./3);

k_0/data/get_data9.m

@@ -1,6 +1,8 @@
 function [f,grad_f_r,grad_f_z,u,grad_u_r,grad_u_z] = get_data9()
 %GET_U_DATA9 Get u and f function handles
 %   u = r^(5/3)
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u = @(r,z) r.^(5./3);
 grad_u_r =@(r,z) (5./3).*r.^(2./3);

k_0/p1/basis_functions_weighted_HL_k_0_p1.m

@@ -14,7 +14,7 @@
 %
 % Outputs:
 %     basis - a matrix representing piece-wise basis functions for each node
-%         in each triangle. basis(i,:,T) represents the pieceiwise basis 
+%         in each triangle. basis(:,i,T) represents the pieceiwise basis 
 %         function for the ith node in triangle T. 
 %
 % Author: Nicole Stock

k_1/data/get_data_1.m

@@ -8,6 +8,9 @@
 %   f = [ -15r^2 + 8r + n^2r^2 - n^2r
 %         2nr^2 - 2nr
 %         0                           ]
+% Author: Nicole Stock
+% Date: Fall 2020
+
 u_vec_r = @(r,z) r.^4 - r.^3;
 u_vec_th = @(r,z) 0;
 u_vec_z = @(r,z) 0;

k_1/lowest_order/create_B_weighted_HL_k_1_p1.m

@@ -1,6 +1,6 @@
 function B = create_B_weighted_HL_k_1_p1(p,t,ed,t_ed,basis_nodes,basis_edges,n)
 % CREATE_B_WEIGHTED_HL_K_1_P1 - Create B matrix
-%   Hodge Laplacian k = 1 case, P1
+%   Hodge Laplacian k = 1 case, lowest order
 %   (grad_rz^n(phi_i), zeta_j)_r where {phi_k}k=1->N is the basis for Ah
 %     and {zeta_l}l=1->N+Ne is the basis for Bh
 %   (Ah is the weighted P1 space)
@@ -55,7 +55,7 @@
 
     [R,Z,Wr,Wz] = triquad(7, coordinates);
 
-    % integrate for each pair of edges + 1 in the triangle
+    % integrate for each pair of basis functions in the triangle
     for i = 1:3
         for j = 1:6
             I = basis_nodes(:,i,T);

k_1/lowest_order/create_F_weighted_HL_k_1_p1.m

@@ -30,7 +30,7 @@
 %     weight
 %
 % Outputs:
-%     S - S matrix used to solve system of equations to approximate
+%     F - F matrix used to solve system of equations to approximate
 %         solution
 %
 % Author: Nicole Stock

k_1/lowest_order/create_S_weighted_HL_k_1_p1.m

@@ -54,7 +54,7 @@
 
     [R,Z,Wr,Wz] = triquad(7, coordinates);
 
-    % integrate for each pair of edges + 1 in the triangle
+    % integrate for each pair of basis functions in the triangle
     for i = 1:6
         for j = i:6
             if i <=3

k_1/lowest_order/errors_exact_weighted_HL_k_1_p1.m

@@ -4,7 +4,7 @@
 %   Hodge Laplacian k = 1 case, P1
 %
 % Syntax:
-%     [err,grad_err,max_err] = 
+%     [err_u,err_s] = 
 %         errors_exact_weighted_HL_k_1_p1
 % Inputs:
 %     p - a 2xNumNodes matrix representing nodal coordinates.

k_1/lowest_order/weighted_HL_k_1_e.m

@@ -1,9 +1,9 @@
 function [err_u,err_s] = weighted_HL_k_1_e(f_vec_r,f_vec_th,f_vec_z,gd,sf,ns,mesh,u_vec_r,u_vec_th,u_vec_z,s,n)
-%WEIGHTED_HL_K_1_E Hodge Laplacian k = 1 P1 Finite Element Method.
+%WEIGHTED_HL_K_1_E Hodge Laplacian k = 1 lowest order Finite Element Method.
 %   This program is set up to be given an exact solution.
-%   Hodge Laplacian k = 1 case, P1
-%   {phi_i}i=1->N is the basis for Ah
-%   {zeta_j}j=1->N+Ne is the basis for Bh
+%   Hodge Laplacian k = 1 case, lowest order
+%   {phi_i}i=1->N is the basis for Ah0
+%   {zeta_j}j=1->N+Ne is the basis for Bh0
 %   (Ah is the weighted P1 space)
 %   (Bh is the weighted fourier modified Nedelec and P1 space)
 %   Solve for (s,u) in (Ah x Bh) s.t.
@@ -14,6 +14,8 @@
 %
 % Syntax:
 %     [err] = weighted_HL_k_1_e(f_vec_r,f_vec_th,f_vec_z,gd,sf,ns,mesh,u_vec_r,u_vec_th,u_vec_z,s,n)
+%
+% Inputs:
 %     f_vec_r - given function r component
 %     f_vec_th - given function theta component
 %     f_vec_z - given function z component
@@ -31,11 +33,11 @@
 % Usage Exampled:
 %    addpath ../../data ../data/
 %    n = 1;
-%    [u_vec_r,u_vec_th,u_vec_z,s,f_vec_r,f_vec_th,f_vec_z] = get_data_1(n)
+%    [u_vec_r,u_vec_th,u_vec_z,s,f_vec_r,f_vec_th,f_vec_z] = get_data_1(n);
 %    mesh = 7;
 %    pdepoly([0,1,1,0], [0,0,1,1]);
 %       (OR) [gd,sf,ns] = get_gd_sf_ns([0,1,1,0],[0,0,1,1]);
-%    [err_u,err_s] = weighted_HL_k_1_e(f_vec_r,f_vec_th,f_vec_z,gd,sf,ns,mesh,u_vec_r,u_vec_th,u_vec_z,s,n)
+%    [err_u,err_s] = weighted_HL_k_1_e(f_vec_r,f_vec_th,f_vec_z,gd,sf,ns,mesh,u_vec_r,u_vec_th,u_vec_z,s,n);
 % Dependencies:
 %    find_edge_connectivity.m
 %    basis_functions_weighted_modified_nedelec_and_p1.m
@@ -52,6 +54,7 @@
 addpath('../../');
 addpath('../../modified_weighted_nedelec_pk/p1/');
 addpath('../../nedelec/weighted_lowest_order/')
+addpath('../../k_0/p1/');
 
 model=createpde(1);
 g=decsg(gd,sf,ns);

k_2/data/get_data_1.m

@@ -10,6 +10,8 @@
 %   f = [ 3n^2 - (3n^2)/r + 6n - (4n)/r - 9
 %         -3n^2 + (2n^2)/r - 6n + (6n)/r + 9
 %         0      ]
+% Author: Nicole Stock
+% Date: Fall 2020
 
 s_vec_r = @(r,z) 3.*r.*(r-1); % 3.*r.^2 - 3.*r
 s_vec_th = @(r,z) -3.*r.^2 + 2.*r;

k_2/lowest_order/create_F_weighted_HL_k_2_p1.m

@@ -29,7 +29,7 @@
 %     f_vec_z - given function z component
 %
 % Outputs:
-%     S - S matrix used to solve system of equations to approximate
+%     F - F matrix used to solve system of equations to approximate
 %         solution
 %
 % Author: Nicole Stock
@@ -87,4 +87,4 @@
 
 F = sparse(i_vec,j_vec,s_vec,edges+triangles,1);
 
-% end
+% end

k_2/lowest_order/create_S_weighted_HL_k_2_p1.m

@@ -1,6 +1,6 @@
 function S = create_S_weighted_HL_k_2_p1(p,t,ed,t_ed,basis_RT_edges,basis_triangles)
 % CREATE_S_WEIGHTED_HL_K_2_P1 - Create S matrix
-%   Hodge Laplacian k = 2 case, P1
+%   Hodge Laplacian k = 2 case, lowest order
 %   (div_rz^n(psi_i), div_rz^n(psi_j))_r where {psi_j}j=1->Ne+Nt is the basis for Ch
 %   (Ch is the weighted fourier Raviart Thomas space)
 %
@@ -26,7 +26,7 @@
 %         function for the Tth triangle.
 %
 % Outputs:
-%     B - B matrix used to solve system of equations to approximate
+%     S - S matrix used to solve system of equations to approximate
 %         solution
 %
 % Author: Nicole Stock
@@ -99,4 +99,4 @@
 
 S = sparse(i_vec,j_vec,s_vec,edges+triangles,edges+triangles);
 
-% end
+% end

k_2/lowest_order/mass_matrix_weighted_HL_k_2_p1.m

@@ -1,6 +1,6 @@
 function mass_matrix = mass_matrix_weighted_HL_k_2_p1(p,t,ed,t_ed,basis_nodes,basis_edges,n)
 % MASS_MATRIX_WEIGHTED_HL_K_2_P1 - Create mass matrix
-%   Hodge Laplacian k = 2 case, P1
+%   Hodge Laplacian k = 2 case, lowest order
 %   (zeta_i, zeta_j)_r where {zeta_k}k=1->(N+Ne) is the basis for Bh
 %   (Bh is the weighted fourier modified Nedelec and P1 space)
 %
@@ -112,4 +112,4 @@
 end
 
 mass_matrix = sparse(i_vec,j_vec,s_vec,nodes+edges,nodes+edges);
-% end
+% end

k_2/lowest_order/weighted_HL_k_2_e.m

@@ -1,9 +1,9 @@
 function [err_u,err_s] = weighted_HL_k_2_e(f_vec_r,f_vec_th,f_vec_z,gd,sf,ns,mesh,u_vec_r,u_vec_th,u_vec_z,s_vec_r,s_vec_th,s_vec_z,n)
-%WEIGHTED_HL_K_1_E Hodge Laplacian k = 1 P1 Finite Element Method.
+%WEIGHTED_HL_K_2_E Hodge Laplacian k = 2 lowest order Finite Element Method.
 %   This program is set up to be given an exact solution.
-%   Hodge Laplacian k = 2 case, P1
-%   {zeta_j}j=1->N+Ne is the basis for Bh
-%   {psi_i}i=1->Ne+Nt is the basis for Ch
+%   Hodge Laplacian k = 2 case, lowest order
+%   {zeta_j}j=1->N+Ne is the basis for Bh0
+%   {psi_i}i=1->Ne+Nt is the basis for Ch0
 %   (Bh is the weighted fourier modified Nedelec and P1 space)
 %   (Ch is the weighted fourier Raviart Thomas space)
 %   Solve for (s,u) in (Bh x Ch) s.t.

k_3/lowest_order/errors_exact_weighted_HL_k_3_p1.m

@@ -93,9 +93,7 @@
     % find L2 Error for p
     integrand =@(r,z) ((p_exact(r,z) - p_h(T)).^2).*r;
 
-    integral_p = integral_p + Wx'*feval(integrand,X,Y)*Wy;    
-
-
+    integral_p = integral_p + Wx'*feval(integrand,X,Y)*Wy;
 end
 
 err_z = sqrt(integral_z);

k_3/lowest_order/weighted_HL_k_3_e.m

@@ -1,9 +1,9 @@
 function [err_z,err_p] = weighted_HL_k_3_e(f,gd,sf,ns,mesh,z_vec_r,z_vec_th,z_vec_z,p_exact,n)
-%WEIGHTED_HL_K_3_E Hodge Laplacian k = 3 P1 Finite Element Method.
+%WEIGHTED_HL_K_3_E Hodge Laplacian k = 3 lowest order Finite Element Method.
 %   This program is set up to be given an exact solution.
-%   Hodge Laplacian k = 3 case, P1
-%   {psi_i}i=1->Ne+Nt is the basis for Ch
-%   {chi_j}j=1->Nt is the basis for Dh
+%   Hodge Laplacian k = 3 case, lowest order
+%   {psi_i}i=1->Ne+Nt is the basis for Ch0
+%   {chi_j}j=1->Nt is the basis for Dh0
 %   (Ch is the weighted fourier Raviart Thomas space)
 %   (Dh is the piecewise constant space)
 %   Solve for (z,p) in (Ch x Dh) s.t.

modified_weighted_nedelec_pk/data/p1/get_data_1.m

@@ -6,6 +6,8 @@
 %   F = [ n(r-1) + u_r   ]
 %       [ -2r + 1 + u_th ]
 %       [ u_z            ]
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u_vec_r = @(r,z) z - (1./n).*((1./3).*r.^3 - (1./2).*r.^2);
 u_vec_th = @(r,z) (-1).*n.*z + (1./3).*r.^3 - (1./2).*r.^2;

nedelec/data/weighted/get_data_1.m

@@ -2,6 +2,8 @@
 %GET_DATA_1 Get u vector and f vector
 %   u = [ sin(pi*r) ; cos(pi*r) ]
 %   F = u
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u_vec_r = @(r,z) sin(pi.*r);
 u_vec_z = @(r,z) cos(pi.*z);

nedelec/data/weighted/get_data_2.m

@@ -4,6 +4,8 @@
 %         (1/2)r^2z - rz ]
 %   F = [ (1/3)rz^3 - (1/3)z^3 - 2rz + 2z + r - 1
 %         2z^2 - (z^2)/r + (1/2)r^2z - rz - 2z + z/r ]
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u_vec_r =@(r,z) (1/3).*(r-1).*z.^3;
 u_vec_z =@(r,z) (1/2).*r.^2.*z - r.*z;

nedelec/data/weighted/get_data_3.m

@@ -4,6 +4,8 @@
 %         (-1/2)r^2z^2 + rz^2 ]
 %   F = [ (-1/2)rz^2 + (1/2)z^2 - 2rz + 2z + r - 1 
 %         (-1/2)r^2z^2 + rz^2 + 2z^2 - z^2/r - 2z + z/r ]
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u_vec_r =@(r,z) (-1/2).*r.*z.^2 + (1./2).*z.^2;
 u_vec_z =@(r,z) (-1/2).*r.^2.*z.^2 + r.*z.^2;

raviart_thomas/data/unweighted2D/get_data_1.m

@@ -4,6 +4,8 @@
 %         -(1/2)r^2z^2 + (1/2)rz^2  ]
 %   F = [ (1/3)r^3z^2 - (1/2)r^2z^2 - 2rz^2 + z^2 + 2rz - z
 %         -(1/2)r^2z^2 + (1/2)rz^2 - 2r^2z + 2rz + r^2 - r   ]
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u_vec_r = @(r,z) (1./3).*(r.^3).*(z.^2) - (1./2).*(r.^2).*(z.^2);
 u_vec_z = @(r,z) -(1./2).*(r.^2).*(z.^2) + (1./2).*r.*z.^2;

raviart_thomas/data/unweighted2D/get_data_2.m

@@ -4,6 +4,8 @@
 %         -(1/3)rz^3 + (1/2)rz^2  ]
 %   F = [ (1/3)r^3z^2 - (1/3)r^3z - 2rz^2 + z^2 + 2rz - z
 %         -(1/3)rz^3 + (1/2)rz^2 - 2r^2z + 2rz + r^2 - r  ]
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u_vec_r = @(r,z) (1./3).*(r.^3).*(z.^2) - (1./3).*z.*r.^3;
 u_vec_z = @(r,z) -(1./3).*r.*z.^3 + (1./2).*r.*z.^2;

raviart_thomas/data/weighted/get_data_1.m

@@ -6,6 +6,8 @@
 %   F = [ -rz^2 - z^2 + z
 %         -(n/r)(rz^2 - z^2 - rz + z)
 %         (1/3)rz^3 - (1/2)rz^2 + (1/2)z^2 + (1/3)z^3 - 2rz + 2z + r - 1 ]
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u_vec_r = @(r,z) -r.*z.^2;
 u_vec_th = @(r,z) 0;

raviart_thomas/data/weighted/get_data_2.m

@@ -6,6 +6,8 @@
 %   F = [ (1/2)rz - (1/2)rz^2 - z^2 + z
 %         -(n/r)(rz^2 - z^2 - rz + z)
 %         (1/3)rz^3 - (1/2)rz^2 -2rz + 2z + r - 1 ]
+% Author: Nicole Stock
+% Date: Fall 2020
 
 u_vec_r = @(r,z) (1./2).*r.*z - (1./2).*r.*z.^2;
 u_vec_th = @(r,z) 0;