AN EFFICIENT MULTICOMPUTER ALGORITHM FOR THE SOLUTION OF CHEMICAL PROCESS FLOWSHEETING EQUATIONS

This paper presents a parallel solution method of large sparse systems of linear equations arising in the context of a chemical process flow sheeting application on a message passing multicomputer. To maximize t he performance, the algorithm uses a novel matrix decomposition and so lution method, called parallel two-phased LU decomposition, which sche dules the concurrent tasks in a maximally overlapping manner, and at t he same time, tries to minimize the interprocessor data dependencies a nd obtain optimal load balancing. The forward elimination step is perf ormed concurrently with the parallel two-phased LU decomposition step and backward substitution is parallelized in a piecewise manner. Imple mentation results on an Intel iPSC/2 multicomputer are presented. With 16 processors, speedups of up to 11.3 are observed for relatively lar ge problem sizes and close to 71% processor utilization is achieved de spite the high fraction of sequential operations in the process. Altho ugh this work was motivated by the need to reduce the computational bo ttleneck of the DZINE flowsheeting program, it should also be applicab le to a wide range of scientific and engineering problems where fast a nd efficient solution of large sparse systems of linear equations is r equired.