Alternatives for solving sparse triangular systems on distributed-memory multiprocessors

Abstract

The solution of sparse triangular systems plays an important role in the direct solution of sparse linear equations. This paper evaluates two alternative approaches to performing this computation on distributed-memory multiprocessors. First we consider a traditional approach, which assumes a column distribution of the triangular system among the processors. We find the performance of this approach to be extremely low, for a variety of reasons. We then consider an alternative approach, which assumes a block-column or panel distribution of the triangular system. This alternative is found to provide several important advantages over a column approach. Overall, the panel approach provides as much as a ten-fold parallel performance improvement. Performance results are presented from highly optimized implementations on the iPSC ® 860 system.