An Implementation of A Parallel Iterative Algorithm for the Solution of Large Banded System on A Cluster of Workstations

Abstract

In this paper, we present a parallel iterative solution for large banded systems of linear equations based on incomplete LU-factorization (ILU). A master—workers parallel computing scheme is used. The proposed algorithm incurs reduced storage and communication overhead as compared to previous methods. The reduction in communication overhead has been achieved by pipelining the inter-workers message passing and limiting the communication between master and workers to initial work distribution and final results collection.The performance of the proposed algorithm is evaluated analytically and experimentally using Parallel Virtual Machine (PVM) as a parallel programming environment on a cluster of Linux work-stations. The obtained performance results show that the proposed algorithm exhibits higher efficiency for coarse grain computations corresponding to large matrix sizes and reduced number of processors.