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improve speed of near field computation #1

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ronandrevon opened this issue Jun 3, 2021 · 3 comments
Open

improve speed of near field computation #1

ronandrevon opened this issue Jun 3, 2021 · 3 comments
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@ronandrevon
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By implementing spherical harmonics using the legendre polynomials recurrence formula, the speed of the wave function computation should be improved.

@kitine
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kitine commented Aug 8, 2021

Implementation of the spherical harmonics :

Recurrence formula used for the implementation :
formule3
formule2
formule1

Explenation of the implemented matrix
Capture d’écran 2021-08-09 000925

Implementation of the legendre polynomes
Capture d’écran 2021-08-09 001556

Formula used to implement spherical harmonics
Capture d’écran 2021-08-09 001723

Implementation of the spherical harmonics
Capture d’écran 2021-08-09 001609

@kitine
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kitine commented Aug 8, 2021

Verification of the implementation of the spherical harmonics :
Capture d’écran 2021-08-09 005657
Capture d’écran 2021-08-09 005736

@kitine
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kitine commented Aug 8, 2021

Speed test

For the computation of spherical harmonics with l=10, m=[-10;10]
Using the recurrence formula : 0.004826784133911133 s
Using python's function : 0.16061711311340332 s

For the computation of the total field
Using the recurrence formula : 20.19532084465027 s
Using python's function : 25.091874837875366 s

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