An explicit hybridizable discontinuous Galerkin method for the 3D time-domain Maxwell equations

Georges Nehmetallah (1, 2) , Stéphane Lanteri (1, 2) , Stéphane Descombes (1, 2) , Alexandra Christophe (1, 2)

1 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
2 LJAD - Laboratoire Jean Alexandre Dieudonné

We present an explicit hybridizable discontinuous Galerkin (HDG) method for numerically solving the system of three-dimensional (3D) time-domain Maxwell equations. The method is fully explicit similarly to classical so-called DGTD (Dis-continuous Galerkin Time-Domain) methods, is also high-order accurate in both space and time and can be seen as a generalization of the classical DGTD scheme based on upwind fluxes. We provide numerical results aiming at assessing its numerical convergence properties by considering a model problem and we present preliminary results of the superconvergence property on the H curl norm.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Georges Nehmetallah, Stéphane Lanteri, Stéphane Descombes, Alexandra Christophe. An explicit hybridizable discontinuous Galerkin method for the 3D time-domain Maxwell equations. ICOSAHOM 2018 - International Conference on Spectral and High Order Methods, Jul 2018, London, United Kingdom. ⟨10.1007/978-3-030-39647-3_41⟩. ⟨hal-01955032v2⟩