Comptes Rendus
Numerical Analysis
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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.09.027
François Hermeline 1

1 CEA/DIF, DSSI/SNEC, BP 12, 91680 Bruyères le Châtel, France
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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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[3] F. Bouchut On the discrete conservation of the Gauss–Poisson equation of plasma physics, Commun. Numer. Methods Engrg., Volume 14 (1998), pp. 23-34

[4] F. Hermeline 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] F. Hermeline 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] F. Hermeline A finite volume method for the approximation of diffusion operators on distorted meshes, J. Comput. Phys., Volume 160 (2000), pp. 481-499

[7] F. Hermeline Approximation of diffusion operators with discontinuous tensor coefficients on distorted meshes, Comput. Methods Appl. Mech. Engrg., Volume 192 (2003), pp. 1939-1959

[8] B. Marder A method for incorporating Gauss' law into electromagnetic PIC codes, J. Comput. Phys., Volume 68 (1987), pp. 48-55

[9] K.S. Yee 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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