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Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes

Published online by Cambridge University Press:  15 November 2005

Loula Fezoui ,
Stéphane Lanteri ,
Stéphanie Lohrengel  and
Serge Piperno
Loula Fezoui
Affiliation:
CERMICS, INRIA, BP93, 06902 Sophia-Antipolis Cedex, France. Serge.Piperno@cermics.enpc.fr
Stéphane Lanteri
Affiliation:
CERMICS, INRIA, BP93, 06902 Sophia-Antipolis Cedex, France. Serge.Piperno@cermics.enpc.fr
Stéphanie Lohrengel
Affiliation:
Dieudonné Lab., UNSA, UMR CNRS 6621, Parc Valrose, 06108 Nice Cedex 2, France.
Serge Piperno
Affiliation:
CERMICS, INRIA, BP93, 06902 Sophia-Antipolis Cedex, France. Serge.Piperno@cermics.enpc.fr
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Abstract

A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved for metallic cavities. Convergence is proved for $\mathbb{P}_k$ Discontinuous elements on tetrahedral meshes, as well as a discrete divergence preservation property. Promising numerical examples with low-order elements show the potential of the method.

Keywords

Electromagneticsfinite volume methodsdiscontinuous Galerkin methodscentered fluxesleap-frog time schemeL2 stabilityunstructured meshesabsorbing boundary conditionconvergencedivergence preservation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 6 , November 2005 , pp. 1149 - 1176
Copyright
© EDP Sciences, SMAI, 2005

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