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