Article Dans Une Revue SIAM Journal on Scientific Computing Année : 2026

A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic electromagnetic problems

Résumé

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.

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Dates et versions

hal-05016261 , version 1 (01-04-2025)
hal-05016261 , version 2 (09-05-2025)

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  • HAL Id : hal-05016261 , version 2

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Ari Rappaport, Théophile Chaumont-Frelet, Axel Modave. A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic electromagnetic problems. SIAM Journal on Scientific Computing, In press. ⟨hal-05016261v2⟩
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