High order scalable HDG method fro frequency-domain electromagnetics

Emmanuel Agullo 1 Matthieu Kuhn 1 Stéphane Lanteri 2 Ludovic Moya 2
1 HiePACS - High-End Parallel Algorithms for Challenging Numerical Simulations
LaBRI - Laboratoire Bordelais de Recherche en Informatique, Inria Bordeaux - Sud-Ouest
2 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : Discontinuous Galerkin (DG) methods have ben extensively studied in the last ten years for the numerical solution of the time-domain Maxwell equations. For the numerical treatment of the frequency-domain Maxwell equations, nodal DG methods can also be considered. However, such DG formulations are highly expensive, especially for the discretization of 3d problems, because they lead to a large sparse and undefinite linear system of equations coupling all the degrees of freedom of the unknown physical fields. Different attempts have been made in the recent past to improve the efficiency of DG methods applied to steady-like problems and one promising strategy has been proposed by Cockburn et al. [1] in the form of so-called hybridizable DG formulations. Such HDG methods have then been designed for the system of frequency-domain Maxwell equations [2]-[3]. In this talk, we will report on recent further developments of the HDG method proposed in [3] aiming at improving its accuracy and scalability for large-scale 3d problems. Beside extending the implementation to an arbitrary high and locally defined interpolation order, an algebraic hybrid iterative-direct solution strategy [4] is considered for the hybrid system characterizing the proposed HDG formulation. REFERENCES
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Submitted on : Tuesday, November 29, 2016 - 2:58:40 PM
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Emmanuel Agullo, Matthieu Kuhn, Stéphane Lanteri, Ludovic Moya. High order scalable HDG method fro frequency-domain electromagnetics. Icosahom 2016 - International Conference on Spectral and High Order Methods , Jun 2016, Rio de Janeiro, Brazil. ⟨hal-01404669⟩

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