AParallel Gauss-Seidel Algorithm for Sparse Power Systems Matrices D. P. Ko ester, S. Ranka, and G. C. Fox Scho ol of Computer and Information Science and The Northeast Parallel Architectures Center (NPAC) Syracuse University Syracuse, NY 13244-4100
[email protected],
[email protected],
[email protected] A ComdensedVersion of this Paper was presentedatSuperComputing `94 NPACTechnical Rep ort | SCCS 630 4 April 1994 Abstract We describ e the implementation and p erformance of an ecient parallel Gauss-Seidel algorithm that has b een develop ed for irregular, sparse matrices from electrical p ower systems applications. Although, Gauss-Seidel algorithms are inherently sequential, by p erforming sp ecialized orderings on sparse matrices, it is p ossible to eliminate much of the data dep endencies caused by precedence in the calculations. A two-part matrix ordering technique has b een develop ed | rst to partition the matrix into blo ck-diagonal-b ordered form using diakoptic techniques and then to multi-color the data in the last diagonal blo ck using graph coloring techniques. The ordered matrices often have extensive parallelism, while maintaining the strict precedence relationships in the Gauss-Seidel algorithm. We present timing results for a parallel Gauss-Seidel solver implemented on the Thinking Machines CM-5 distributed memory multi-pro cessor. The algorithm presented here requires active message remote pro cedure calls in order to minimize communications overhead and obtain go o d relative sp eedup. The paradigm used with active messages greatly simpli ed the implementationof this sparse matrix algorithm. 1 Intro duction Wehavedevelop ed an ecient parallel Gauss-Seidel algorithm for irregular, sparse matrices from electrical p ower systems applications.