Using multiple levels of parallelism to enhance the performance of domain decomposition solvers

Large-scale scientific simulations are nowadays fully integrated in many scientific and industrial applications. Many of these simulations rely on modelisations based on PDEs that lead to the solution of huge linear or nonlinear systems of equations involving millions of unknowns. In that context, the use of large high performance computers in conjunction with advanced fully parallel and scalable numerical techniques is mandatory to efficiently tackle these problems. In this paper, we consider a parallel linear solver based on a domain decomposition approach. Its implementation naturally exploits two levels of parallelism, that offers the flexibility to combine the numerical and the parallel implementation scalabilities. The combination of the two levels of parallelism enables an optimal usage of the computing resource while preserving attractive numerical performance. Consequently, such a numerical technique appears as a promising candidate for intensive simulations on massively parallel platforms. The robustness and parallel numerical performance of the solver is investigated on large challenging linear systems arising from the finite element discretization in structural mechanics applications.