2025/05/07 by Rappaport, Ari E., Chaumont-Frelet, Théophile, Modave, Axel
#65F08 #65N22 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2505.04288
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.