Issue |
ESAIM: M2AN
Volume 39, Number 6, November-December 2005
|
|
---|---|---|
Page(s) | 1149 - 1176 | |
DOI | https://doi.org/10.1051/m2an:2005049 | |
Published online | 15 November 2005 |
Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes
1
CERMICS, INRIA, BP93, 06902 Sophia-Antipolis Cedex, France. Serge.Piperno@cermics.enpc.fr
2
Dieudonné Lab., UNSA, UMR CNRS 6621, Parc Valrose, 06108 Nice Cedex 2, France.
Received:
17
August
2004
Revised:
2
July
2005
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
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.
Mathematics Subject Classification: 65M12 / 65M60 / 78-08 / 78A40
Key words: Electromagnetics / finite volume methods / discontinuous Galerkin methods / centered fluxes / leap-frog time scheme / L2 stability / unstructured meshes / absorbing boundary condition / convergence / divergence preservation.
© EDP Sciences, SMAI, 2005
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