An implicit hybridized discontinuous Galerkin method for the 3D time-domain Maxwell equations

Alexandra Christophe-Argenvillier (1, 2, 3) , Stéphane Descombes (1, 2, 3) , Stéphane Lanteri (1, 2, 3)

1 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
2 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
3 LJAD - Laboratoire Jean Alexandre Dieudonné

We present a time-implicit hybridizable discontinuous Galerkin (HDG) method for numerically solving the system of three-dimensional (3D) time-domain Maxwell equations. This method can be seen as a fully implicit variant of classical so-called DGTD (Discontinuous Galerkin Time-Domain) methods that have been extensively studied during the last 10 years for the simulation of time-domain electromagnetic wave propagation. The proposed method has been implemented for dealing with general 3D problems discretized using unstructured tetrahedral meshes. We provide numerical results aiming at assessing its numerical convergence properties by considering a model problem on one hand, and its performance when applied to more realistic problems. We also include some performance comparisons with a centered flux time-implicit DGTD method.

Mots clés: Maxwell's equations; time-domain; implicit time stepping; discontinuous Galerkin; hybridized discontinuous Galerkin

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

Alexandra Christophe-Argenvillier, Stéphane Descombes, Stéphane Lanteri. An implicit hybridized discontinuous Galerkin method for the 3D time-domain Maxwell equations. 2016. ⟨hal-01374521⟩