Resolution strategy for the Hybridizable Discontinuous Galerkin system for solving Helmholtz elastic wave equations

International audienceThe advantage of performing seismic imaging in frequency domain is that it is not necessary tostore the solution at each time step of the forward simulation. Unfortunately, the drawback ofthe Helmholtz equations, when considering 3D realistic elastic cases, lies in solving large linearsystems. 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 developed a Hybridizable DiscontinuousGalerkin 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 ofthe matrix to be inverted only depends on the number of degrees of freedom on each face andon the number of the faces of the mesh, instead of the number of degrees of freedom on each celland on the number of the cells of the mesh as we have for the classical Discontinuous Galerkinmethods (DGm). The solution to the initial problem is then recovered thanks to independentelementwise 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 MassivelyParallel 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 solverswhen solving 3D elastic wave propagation over HDGm