GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Generalized Schwarz splittings
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Computer Methods in Applied Mechanics and Engineering
Applied Numerical Mathematics
Applied Numerical Mathematics - Special issue on massively parallel computing and applications
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Block-Triangular Preconditioners for Saddle Point Problems with a Penalty Term
SIAM Journal on Scientific Computing
A parallel algorithm for multilevel graph partitioning and sparse matrix ordering
Journal of Parallel and Distributed Computing
BILUTM: A Domain-Based Multilevel Block ILUT Preconditioner for General Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
A Multilevel Dual Reordering Strategy for Robust Incomplete LU Factorization of Indefinite Matrices
SIAM Journal on Matrix Analysis and Applications
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The present paper describes the development and the performance of parallel FEM software for solving various CFD problems. Domain decomposition strategy and parallel iterative GMRES solver have been adapted to the universal space-time FEM code FEMTOOL, which allows implementation of any partial differential equation with minor expenses. The developed data structures, the static load balancing and the inter-processor communication algorithms have been particularly suited for homogeneous distributed memory PC clusters. The universality of the considered parallel algorithms has been validated solving applications described by the Poisson equation, by the convective transport equation and by the Navier-Stokes equations. Three typical benchmark problems have been solved in order to perform the efficiency study. The performance of parallel computations, the speed-up and the efficiency have been measured on three BEOWULF PC clusters as well as on the cluster of IBM RISC workstations and on the IBM SP2 supercomputer.