Hybridizable discontinuous Galerkin method for the two-dimensional frequency-domain elastic wave equations

Marie Bonnasse-Gahot 1, 2 Henri Calandra 3 Julien Diaz 2 Stéphane Lanteri 1
1 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
2 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : Discontinuous Galerkin (DG) methods are nowadays actively studied and increasingly exploited for the simulation of large-scale time-domain (i.e. unsteady) seismic wave propagation problems. Although theoretically applicable to frequency-domain problems as well, their use in this context has been hampered by the potentially large number of coupled unknowns they incur, especially in the three-dimensional case, as compared to classical continuous finite element methods. In this paper, we address this issue in the framework of so-called hybridizable discontinuous Galerkin (HDG) formulations. As a first step, we study a HDG method for the resolution of the frequency-domain elastic wave equations in the two-dimensional case. We describe the weak formulation of the method and provide some implementation details. The proposed HDG method is assessed numerically including a comparison with a classical upwind flux-based DG method, showing better overall computational efficiency as a result of the drastic reduction of the number of globally coupled unknowns in the resulting discrete HDG system.
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Marie Bonnasse-Gahot, Henri Calandra, Julien Diaz, Stéphane Lanteri. Hybridizable discontinuous Galerkin method for the two-dimensional frequency-domain elastic wave equations. Geophysical Journal International, Oxford University Press (OUP), 2018, 213 (1), pp.637--659. ⟨10.1093/gji/ggx533⟩. ⟨hal-01656440⟩

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