A finite volume method for the approximation of Maxwell's equations in two space dimensions on arbitrary meshes

Authors:
F. Hermeline;S. Layouni;P. Omnes
Affiliations:
Commissariat í l'énergie atomique, Centre DAM-Ile de France, DSSI, Bruyères-le-Chítel, 91297 Arpajon Cedex, France;CEA Saclay, DEN/DM2S/SFME, 91191 Gif Sur Yvette Cedex, France;CEA Saclay, DEN/DM2S/SFME, 91191 Gif Sur Yvette Cedex, France
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

A new finite volume method is presented for discretizing the two-dimensional Maxwell equations. This method may be seen as an extension of the covolume type methods to arbitrary, possibly non-conforming or even non-convex, n-sided polygonal meshes, thanks to an appropriate choice of degrees of freedom. An equivalent formulation of the scheme is given in terms of discrete differential operators obeying discrete duality principles. The main properties of the scheme are its energy conservation, its stability under a CFL-like condition, and the fact that it preserves Gauss' law and divergence free magnetic fields. Second-order convergence is demonstrated numerically on non-conforming and distorted meshes.