A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic electromagnetic problems
Abstract
The CHDG method is a hybridizable discontinuous Galerkin (HDG) finite element method suitable for the iterative solution of time-harmonic wave propagation problems. Hybrid unknowns corresponding to transmission variables are introduced at the element interfaces and the physical unknowns inside the elements are eliminated, resulting in a hybridized system with favorable properties for fast iterative solution. In this paper, we extend the CHDG method, initially studied for the Helmholtz equation, to the time-harmonic Maxwell equations. We prove that the local problems stemming from hybridization are well-posed and that the fixed-point iteration naturally associated to the hybridized system is contractive. We propose a 3D implementation with a discrete scheme based on nodal basis functions. The resulting solver and different iterative strategies are studied with several numerical examples using a high-performance parallel C++ code.
Cite
@article{arxiv.2505.04288,
title = {A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic electromagnetic problems},
author = {Ari E. Rappaport and Théophile Chaumont-Frelet and Axel Modave},
journal= {arXiv preprint arXiv:2505.04288},
year = {2025}
}