Comparison of solvers performance when solving the 3D Helmholtz elastic wave equations using the Hybridizable Discontinuous Galerkin method

Marie Bonnasse-Gahot 1 Henri Calandra 2 Julien Diaz 3, 1 Stephane 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 Total E&P
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. Unfortunately, the drawback of the Helmholtz equations, when considering 3D realistic elastic cases, lies in solving large linear systems. This represents today a challenging task even with the use of High Performance Computing (HPC). To reduce the size of the global linear system, we developped 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, instead of the number of degrees of freedom on each cell and on the number of the cells of the mesh as we have for the classical Discontinuous Galerkin methods (DGm). The solution to the initial problem is then recovered thanks to independent elementwise calculation. As the HDG global matrix is very sparse, we focus on a suitable solver for this kind of matrix. We tested two linear solvers: a parallel sparse direct solver MUMPS ( MUltifrontal Massively Parallel sparse direct Solver) and a hybrid solver MaPHyS (Massively Parallel Hybrid Solver) which combines direct and iterative methods. We compared the performance of the two solvers when solving 3D elastic wave propagation over HDGm.
Keywords : Direct solvers Hybrid solvers Seismic Imaging Harmonic domain Elastic waves Hybridizable discontinuous Galerkin method
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Marie Bonnasse-Gahot, Henri Calandra, Julien Diaz, Stephane Lanteri. Comparison of solvers performance when solving the 3D Helmholtz elastic wave equations using the Hybridizable Discontinuous Galerkin method. Workshop DIP - Depth Imaging Partnership, Oct 2016, Houston, United States. ⟨hal-01400656⟩

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