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

Hassan Fahs (1) , Stephane Lanteri (1)

1 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media

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.

Mots clés: Time-domain Maxwell's equations; Discontinuous Galerkin method; Explicit time integration; Non-conforming meshes; Computational electromagnetism

Domaines: Physique mathématique [math-ph]; Analyse numérique [math.NA]; Electromagnétisme

Hassan Fahs, Stephane Lanteri. A high-order non-conforming discontinuous Galerkin method for time-domain electromagnetics. Journal of Computational and Applied Mathematics, 2010, 234 (4), pp.1088-1096. ⟨10.1016/j.cam.2009.05.015⟩. ⟨hal-00600468⟩