[Une méthode de volumes finis pour les équations de Maxwell en milieu inhomogène sur des maillages arbitraires.]
On présente une nouvelle méthode d'approximation du type volumes finis pour les équations de Maxwell en milieu inhomogène. Cette méthode possède plusieurs avantages : (i) elle permet d'utiliser des maillages de polygones quelconques même très déformés ou non convexes ; (ii) elle préserve la loi de Gauss ; (iii) elle fournit un système differentiel explicite ; (iv) elle généralise la méthode des différences finies usuelle et les méthodes de volumes finis sur des maillages de Delaunay–Voronoi.
We present a new finite volume method for solving Maxwell equations in inhomogeneous media. This method has several advantages: (i) it allows even distorted or non-convex arbitrary polygonal meshes to be used; (ii) it preserves the Gauss law; (iii) it leads to an explicit differential system; (iv) it generalizes the standard finite difference method and the finite volume method on Delaunay–Voronoi meshes.
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@article{CRMATH_2004__339_12_893_0,
author = {Hermeline, Fran\c{c}ois},
title = {A finite volume method for solving {Maxwell} equations in inhomogeneous media on arbitrary meshes},
journal = {Comptes Rendus. Math\'ematique},
pages = {893--898},
publisher = {Elsevier},
volume = {339},
number = {12},
year = {2004},
doi = {10.1016/j.crma.2004.09.027},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.09.027/}
}
TY - JOUR AU - Hermeline, François TI - A finite volume method for solving Maxwell equations in inhomogeneous media on arbitrary meshes JO - Comptes Rendus. Mathématique PY - 2004 SP - 893 EP - 898 VL - 339 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.09.027/ DO - 10.1016/j.crma.2004.09.027 LA - en ID - CRMATH_2004__339_12_893_0 ER -
%0 Journal Article %A Hermeline, François %T A finite volume method for solving Maxwell equations in inhomogeneous media on arbitrary meshes %J Comptes Rendus. Mathématique %D 2004 %P 893-898 %V 339 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.09.027/ %R 10.1016/j.crma.2004.09.027 %G en %F CRMATH_2004__339_12_893_0
Hermeline, François. A finite volume method for solving Maxwell equations in inhomogeneous media on arbitrary meshes. Comptes Rendus. Mathématique, Tome 339 (2004) no. 12, pp. 893-898. doi : 10.1016/j.crma.2004.09.027. http://www.numdam.org/articles/10.1016/j.crma.2004.09.027/
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