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Mathematics > Numerical Analysis

arXiv:2212.11529 (math)
[Submitted on 22 Dec 2022 (v1), last revised 7 Sep 2023 (this version, v2)]

Title:A hybridizable discontinuous Galerkin method with characteristic variables for Helmholtz problems

Authors:A. Modave, T. Chaumont-Frelet
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Abstract:A new hybridizable discontinuous Galerkin method, named the CHDG method, is proposed for solving time-harmonic scalar wave propagation problems. This method relies on a standard discontinuous Galerkin scheme with upwind numerical fluxes and high-order polynomial bases. Auxiliary unknowns corresponding to characteristic variables are defined at the interface between the elements, and the physical fields are eliminated to obtain a reduced system. The reduced system can be written as a fixed-point problem that can be solved with stationary iterative schemes. Numerical results with 2D benchmarks are presented to study the performance of the approach. Compared to the standard HDG approach, the properties of the reduced system are improved with CHDG, which is more suited for iterative solution procedures. The condition number of the reduced system is smaller with CHDG than with the standard HDG method. Iterative solution procedures with CGNR or GMRES required smaller numbers of iterations with CHDG.
Subjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph)
Cite as: arXiv:2212.11529 [math.NA]
  (or arXiv:2212.11529v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2212.11529
Journal reference: Journal of Computational Physics 493 (2023) 112459
Related DOI: https://doi.org/10.1016/j.jcp.2023.112459

Submission history

From: Axel Modave [view email]
[v1] Thu, 22 Dec 2022 08:15:27 UTC (3,053 KB)
[v2] Thu, 7 Sep 2023 19:27:15 UTC (3,264 KB)
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