Finite element computations on cluster of PC's and workstations

Authors:
A. N. Spyropoulos;J. A. Palyvos;A. G. Boudouvis
Affiliations:
Department of Chemical Engineering, National Technical University of Athens, Athens, Greece;Department of Chemical Engineering, National Technical University of Athens, Athens, Greece;Department of Chemical Engineering, National Technical University of Athens, Athens, Greece
Venue:
EURO-PDP'00 Proceedings of the 8th Euromicro conference on Parallel and distributed processing
Year:
2000

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Abstract

In the last decade distributed processing on cluster of PC's and workstations became a popular alternative way for parallel computations due to their low cost compared with the cost of parallel supercomputers. The most important factor that limits the parallel efficiency of an algorithms running on a cluster is the low bandwidth and high latency of the network that interconnects the computers. Specially designed parallel algorithms must be applied that have low communication overhead. A parallel method on Galerkin/finite element computations on cluster of PC's and workstations is presented. This method is based on a parallel preconditioned Krylov-type iterative solver for the solution of large, sparse and nonsymmetric equation systems. Two important aspects of the method are addressed: the storage of the coefficient matrix of the system and of the preconditioning matrix, and the performance of the preconditioner. The matrix storage affects the parallel efficiency of the matrix vector product. The preconditioner contributes to the parallel efficiency and is of critical importance for the convergence rate of the iterative method. The performance of the method is analyzed in terms of parallel speedup, storage efficiency and convergence rate.