Parallel solution of sparse algebraic equations

Abstract

Two methods that have been studied for solving large, sparse sets of algebraic equations connected with power system problems, the multiple factoring method and the W-matrix method, are shown to be two independent methods of explaining equivalent computational procedures. The forward and backward substitution part of these methods are investigated using parallel processing techniques on commercially available computers. The results are presented from testing the proposed methods on two local memory machines, the Intel iPSC/1 and iPSC/860 hypercubes, and a shared memory machine, the Sequent SymmetryS81. With the iPSC/1, which is characterised by its slow communication rate and high communication overhead for a short message, the best speedup obtained is less than 2.5, and that was with only 8 of the 16 available processors in use. The iPSC/860, a more advanced model of the iPSC family, is even worse as far as these parallel methods are concerned. Much better results were obtained on the Sequent Symmetry where a speedup of 7.48 was obtained with 16 processors