Finite element computations on cluster of PCs and workstations

Abstract

In the last decade distributed processing on clusters of PCs and workstations have become a popular alternative way for parallel computations due to their low cost compared to parallel supercomputers. The most important factor that limits the parallel efficiency of an algorithm 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 clusters of PCs 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 analysed in terms of parallel speedup, storage efficiency and convergence rate.