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.
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.
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François Hermeline 1
@article{CRMATH_2004__339_12_893_0, author = {Fran\c{c}ois Hermeline}, 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}, }
TY - JOUR AU - François Hermeline 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 DO - 10.1016/j.crma.2004.09.027 LA - en ID - CRMATH_2004__339_12_893_0 ER -
François Hermeline. A finite volume method for solving Maxwell equations in inhomogeneous media on arbitrary meshes. Comptes Rendus. Mathématique, Volume 339 (2004) no. 12, pp. 893-898. doi : 10.1016/j.crma.2004.09.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.027/
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