A Parallel Gauss-Seidel Algorithm for Sparse Power Systems Matrices

We describe the implementation and performance of an e cient parallel Gauss-Seidel algorithm that has been developed for irregular, sparse matrices from electrical power systems applications. Although, Gauss-Seidel algorithms are inherently sequential, by performing specialized orderings on sparse matrices, it is possible to eliminate much of the data dependencies caused by precedence in the calculations. A two-part matrix ordering technique has been developed | rst to partition the matrix into block-diagonal-bordered form using diakoptic techniques and then to multi-color the data in the last diagonal block 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-processor. The algorithm presented here requires active message remote procedure calls in order to minimize communications overhead and obtain good relative speedup. The paradigm used with active messages greatly simpli ed the implementation of this sparse matrix algorithm.