Modeling of elastic Helmholtz equations by hybridizable discontinuous Galerkin method (HDG) for geophysical applications

Marie Bonnasse-Gahot 1 Henri Calandra 2 Julien Diaz 1, 3 Stéphane Lanteri 4
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
2 CSTJF - TOTAL-Scientific and Technical Center Jean Féger
3 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
4 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 : The advantage of performing seismic imaging in frequency domain is that it is not necessary to store the solution at each time step of the forward simulation. But the main drawback of the elastic Helmholtz equations, when considering 3D realistic elastic case, lies in solving large linear systems, which represents today a challenging tasks even with the use of high performance computing (HPC). To reduce the size of the global linear system, we develop a hybridizable discontinuous Galerkin method (HDGm). It consists in expressing the unknowns of the initial problem in function of the trace of the numerical solution on each face of the mesh cells. In this way the size of the matrix to be inverted only depends on the number of degrees of freedom on each face and on the number of the faces of the mesh. The solution to the initial problem is then recovered thanks to independent elementwise calculation.
Keywords : Harmonic domain Elastic Waves Discontinuous Galerkin Method Hybridizable Discontinuous Galerkin seismic imaging
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Conference papers
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https://hal.inria.fr/hal-01207897
Contributor : Marie Bonnasse-Gahot <>
Submitted on : Friday, October 2, 2015 - 2:04:09 PM
Last modification on : Friday, June 7, 2019 - 3:16:15 PM

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  • HAL Id : hal-01207897, version 1

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Marie Bonnasse-Gahot, Henri Calandra, Julien Diaz, Stéphane Lanteri. Modeling of elastic Helmholtz equations by hybridizable discontinuous Galerkin method (HDG) for geophysical applications. 5th workshop France-Brazil HOSCAR, Sep 2015, Nice, France. ⟨hal-01207897⟩

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