A multifrontal algorithm for the solution of large systems of equations using network-based parallel computing

Abstract

A multifrontal algorithm for solving large sparse systems of equations has been developed and implemented in a distributed computing environment. The Parallel Virtual Machine (PVM) software was used to combine several networked workstations into a single parallel computational resource. The motivation for this work was the need for solving efficiently the large systems of equations arising in Finite Element Analysis of transport and reaction processes underlying the chemical vapor deposition of thin films. Both out-of-core and in-core computations produce significant speedups for a flow and heat transfer problem using up to 7 networked workstations in a parallel mode. The performance of the algorithm was found to deteriorate rapidly as the granularity of the problem decreased. Thus, it is desirable to scale up the problem size with the number of processors to achieve respectable speedups with the proposed multifrontal technique. The intrinsic fault tolerance capabilities of the PVM software were implemented for completing the computations when one or more workstations became unavailable during a run.