Parallel multigrid methods for the calculation of unsteady flows on unstructured grids: algorithmic aspects and parallel performances on clusters of PCs

We report on our efforts towards the design of efficient parallel hierarchical iterative methods for the solution of sparse and irregularly structured linear systems resulting from CFD applications. The solution strategies considered here share a central numerical kernel which consists in a linear multigrid by volume agglomeration method. Starting from this method, we study two parallel solution strategies. The first variant results from a direct intra-grid parallelization of multigrid operations on coarse grids. The second variant is based on an additive Schwarz domain decomposition algorithm which is formulated at the continuous level through the introduction of specific interface conditions. In this variant, the linear multigrid by volume agglomeration method is used to approximately solve the local systems obtained at each iteration of the Schwarz algorithm. As a result, the proposed hybrid domain decomposition/multigrid method can be viewed as a particular form of parallel multigrid in which multigrid acceleration is applied on a subdomain basis, these local calculations being coordinated by an appropriate domain decomposition iteration at the global level. The parallel performances of these two parallel multigrid methods are evaluated through numerical experiments that are performed on several clusters of PCs with different computational nodes and interconnection networks.