GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A class of implicit upwind schemes for Euler simulations with unstructured meshes
Journal of Computational Physics
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Multigrid
High-performacne parallel implicit CFD
Parallel Computing - Special issue on parallel computing in aerospace
Directional Agglomeration Multigrid Techniques for High-Reynolds Number Viscous Flows
Directional Agglomeration Multigrid Techniques for High-Reynolds Number Viscous Flows
Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing
SIAM Journal on Scientific Computing
Parallel implementation of 3D global MHD simulations for Earth's magnetosphere
Computers & Mathematics with Applications
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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.