Discontinuous Galerkin methods for solving Helmholtz isotropic wave equations for seismic applications

Abstract : Seismic applications require to solve wave equations in heterogeneous media. Thus we choose to focus on the Helmholtz wave equations resolution in isotropic heterogenous media using Galerkin discontinuous methods (DG). To do that we select three DG methods: the DG method with centered flux, the DG method with upwind flux and the hybridizable DG method in order to compare the different results. The principal issue is to obtain the better solution reducing at the maximum time and memory costs. The first step of our work was to complete a program for solving Helmholtz wave equations using DG methods with centered flux and upwind flux. To test the program and compare results the two first results, I used two test-cases: the test-case of plane wave and the one of the diffraction by a circle. The second step is currently to develop the hybridizable DG formulation for Helmholtz wave equations in time-harmonic domain.
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Marie Bonnasse-Gahot, Stephane Lanteri, Julien Diaz, Henri Calandra. Discontinuous Galerkin methods for solving Helmholtz isotropic wave equations for seismic applications. HOSCAR - 3rd Brazil-French workshop on High performance cOmputing and SCientific dAta management dRiven by highly demanding applications (INRIA-CNPq), Sep 2013, Bordeaux, France. 2013. ⟨hal-00929971⟩

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