A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic electromagnetic problems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910931129204736 |
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| author | Rappaport, Ari E. Chaumont-Frelet, Théophile Modave, Axel |
| author_facet | Rappaport, Ari E. Chaumont-Frelet, Théophile Modave, Axel |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_04288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic electromagnetic problems Rappaport, Ari E. Chaumont-Frelet, Théophile Modave, Axel Numerical Analysis 65F08, 65N22, 65N30 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. |
| title | A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic electromagnetic problems |
| topic | Numerical Analysis 65F08, 65N22, 65N30 |
| url | https://arxiv.org/abs/2505.04288 |