Implementation and performance assessment of a parallel solver for sparse linear systems of equations and rules for optimal solution

Abstract

Many computational algorithms in science and engineering give rise to large sparse linear systems of equations which need to be solved as efficiently as possible. As the size of the problems of interest increases, it becomes necessary to consider exploiting multiprocessors to solve these systems. This paper reports on the implementation of a parallel solver for sparse linear systems of equations and proposes simple formulas for predicting the speedup in terms of the size of the linear system and number of processors in the cluster. The iterative solvers considered in this paper are i – Conjugate Gradient Squared Method (CGS), ii – Generalised Minimal Residual Method (GMRES) and iii – the Transpose Free Quasi-Minimal Residual Method (TFQMR) from the Aztec library implemented with the MPI interface and Parallel Knoppix based cluster.