A postprocessing technique for a discontinuous Galerkin discretization of time-dependent Maxwell's equations - Inria - Institut national de recherche en sciences et technologies du numérique
Preprints, Working Papers, ... Year : 2020

A postprocessing technique for a discontinuous Galerkin discretization of time-dependent Maxwell's equations

Abstract

We present a novel postprocessing technique for a discontinuous Galerkin (DG) discretization of time-dependent Maxwell's equations that we couple with an explicit Runge-Kutta time-marching scheme. The postprocessed electromagnetic field converges one order faster than the unprocessed solution in the H(curl)-norm. The proposed approach is local, in the sense that the enhanced solution is computed independently in each cell of the computational mesh, and at each time step of interest. As a result, it is inexpensive to compute, especially if the region of interest is localized, either in time or space. The key ideas behind this postprocessing technique stem from hybridizable discontinuous Galerkin (HDG) methods , which are equivalent to the analyzed DG scheme for specific choices of penalization parameters. We present several numerical experiments that highlight the superconvergence properties of the postprocessed electromagnetic field approximation.
Fichier principal
Vignette du fichier
nehmetallah_chaumontfrelet_descombes_lanteri_2020a.pdf (757.03 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-02956882 , version 1 (03-10-2020)

Identifiers

  • HAL Id : hal-02956882 , version 1

Cite

Georges Nehmetallah, Théophile Chaumont-Frelet, Stéphane Descombes, Stéphane Lanteri. A postprocessing technique for a discontinuous Galerkin discretization of time-dependent Maxwell's equations. 2020. ⟨hal-02956882⟩
124 View
141 Download

Share

More