[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.
Accepté le :
Publié le :
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/
[1] On a finite element method for solving the three-dimensional Maxwell equations, J. Comput. Phys., Volume 109 (1993), pp. 222-237
[2] Numerical approximation of the Maxwell equations in inhomogeneous media by a P1 conforming finite element method, J. Comput. Phys., Volume 128 (1996), pp. 363-380
[3] On the discrete conservation of the Gauss–Poisson equation of plasma physics, Commun. Numer. Methods Engrg., Volume 14 (1998), pp. 23-34
[4] Two coupled particle-finite volume methods using Delaunay–Voronoi meshes for the approximation of Vlasov–Poisson and Vlasov–Maxwell equations, J. Comput. Phys., Volume 106 (1993) no. 1, pp. 1-18
[5] Une méthode de volumes finis pour les équations elliptiques du second ordre, C. R. Acad. Sci. Paris, Ser. I, Volume 326 (1998), pp. 1433-1436
[6] A finite volume method for the approximation of diffusion operators on distorted meshes, J. Comput. Phys., Volume 160 (2000), pp. 481-499
[7] Approximation of diffusion operators with discontinuous tensor coefficients on distorted meshes, Comput. Methods Appl. Mech. Engrg., Volume 192 (2003), pp. 1939-1959
[8] A method for incorporating Gauss' law into electromagnetic PIC codes, J. Comput. Phys., Volume 68 (1987), pp. 48-55
[9] Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Antennas and Propag., Volume 14 (1966), pp. 302-307
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