A high-order non-conforming discontinuous Galerkin method for time-domain electromagnetics

Authors:
Hassan Fahs;Stéphane Lanteri
Affiliations:
INRIA, 2004 Route des Lucioles, BP 93, F-06902 Sophia Antipolis Cedex, France;INRIA, 2004 Route des Lucioles, BP 93, F-06902 Sophia Antipolis Cedex, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

In this paper, we discuss the formulation, stability and validation of a high-order non-dissipative discontinuous Galerkin (DG) method for solving Maxwell's equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter element boundaries, with either a second-order or a fourth-order leap-frog time integration scheme. Moreover, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary-level hanging nodes. The method is proved to be stable and conserves a discrete counterpart of the electromagnetic energy for metallic cavities. Numerical experiments with high-order elements show the potential of the method.