Parallel workstation clusters and MPI for sparse systems in computational science

Abstract

This chapter investigates using a virtual parallel machine formed by the MPI software library to solve a representative class of nonlinear boundary-value problems in Computational Mechanics. The goals of this investigation are to study effectiveness of the workstation cluster in conjunction with the MPI library to solve problems of this nature and to test parallel polynomial preconditioning as a possible means to improve overall algorithm performance for workstation clusters. A parallel domain decomposition scheme is implemented using MPI on a workstation cluster and performance is investigated for a representative problem in computational mechanics. Polynomial preconditioning is also investigated in the chapter. A virtual parallel machine is becoming a viable, easily accessible and cost effective computational resource. This can be achieved most conveniently using Message-Passing libraries since it gives the user more control over an algorithm to achieve higher performance than in the data-parallel and compiler based models. This allows the user to properly decompose a problem to take advantage of special hardware, for example, cache and memory management are issues that cannot be avoided when dealing with present day workstations if good performance is yet to be achieved.