Dans cette note nous nous intéressons à l’analyse de stabilité de la méthode de couches absorbantes parfaitement adaptées (PMLs) pour la propagation d’ondes électromagnétiques en régime transitoire dans un milieu anisotrope décrit par un tenseur diélectrique diagonal. Contrairement aux cas de l’équation d’ondes scalaire 3D et des équations de Maxwell 2D, certaines anisotropies diagonales mènent à l’existence d’ondes inverses qui provoquent des instabilités de la méthode PML. Ce résultat est illustré par des simulations numériques.
The analysis of Cartesian Perfectly Matched Layers (PMLs) in the context of time-domain electromagnetic wave propagation in a 3D unbounded anisotropic homogeneous medium modelled by a diagonal dielectric tensor is presented. Contrary to the 3D scalar wave equation or 2D Maxwell’s equations some diagonal anisotropies lead to the existence of backward waves giving rise to instabilities of the PMLs. Numerical experiments confirm the presented result.
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@article{CRMATH_2021__359_3_249_0,
author = {B\'ecache, \'Eliane and Fliss, Sonia and Kachanovska, Maryna and Kazakova, Maria},
title = {On a surprising instability result of {Perfectly} {Matched} {Layers} for {Maxwell{\textquoteright}s} equations in {3D} media with diagonal anisotropy},
journal = {Comptes Rendus. Math\'ematique},
pages = {249--256},
publisher = {Acad\'emie des sciences, Paris},
volume = {359},
number = {3},
year = {2021},
doi = {10.5802/crmath.165},
language = {en},
url = {http://www.numdam.org/articles/10.5802/crmath.165/}
}
TY - JOUR AU - Bécache, Éliane AU - Fliss, Sonia AU - Kachanovska, Maryna AU - Kazakova, Maria TI - On a surprising instability result of Perfectly Matched Layers for Maxwell’s equations in 3D media with diagonal anisotropy JO - Comptes Rendus. Mathématique PY - 2021 SP - 249 EP - 256 VL - 359 IS - 3 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.165/ DO - 10.5802/crmath.165 LA - en ID - CRMATH_2021__359_3_249_0 ER -
%0 Journal Article %A Bécache, Éliane %A Fliss, Sonia %A Kachanovska, Maryna %A Kazakova, Maria %T On a surprising instability result of Perfectly Matched Layers for Maxwell’s equations in 3D media with diagonal anisotropy %J Comptes Rendus. Mathématique %D 2021 %P 249-256 %V 359 %N 3 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.165/ %R 10.5802/crmath.165 %G en %F CRMATH_2021__359_3_249_0
Bécache, Éliane; Fliss, Sonia; Kachanovska, Maryna; Kazakova, Maria. On a surprising instability result of Perfectly Matched Layers for Maxwell’s equations in 3D media with diagonal anisotropy. Comptes Rendus. Mathématique, Tome 359 (2021) no. 3, pp. 249-256. doi : 10.5802/crmath.165. http://www.numdam.org/articles/10.5802/crmath.165/
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