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Performances Analysis of a Hybridizable Discontinuous Galerkin Solver for the 3D Helmholtz Equations in Geophysical Context
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, Third EAGE Workshop on High Performance Computing for Upstream, Oct 2017, Volume 2017, p.1 - 5
Abstract
Summary
In our work, we consider Discontinuous Galerkin methods (DGm) to solve 3D elastic equations in frequency domain. In 3D, the large size of the linear system represents a challenge even with the use of High Performance Computing (HPC).
Our solution is to develop a new class of DGm, a hybridizable Discontinuous Galerkin method (HDGm). It consists of expressing the unknowns of the initial problem in terms of the trace of the numerical solution on each face of the mesh cells.
We, first, compared the computational performances, in terms of CPU time and memory consumption, of the HDGm with the ones of a classical DGm and of a classical finite elements method (FEm).
Then, since the global matrix of HDGm is very sparse, we also compared performances of the two solvers when solving 3D elastic wave propagation over HDGms: 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.
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