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Conclusions

We have developed a parallel sparse Gauss-Seidel solver with the potential for good relative speedup and relative efficiencies for the very sparse, irregular matrices encountered in electrical power system applications. Block-diagonal-bordered matrix structure offers promise for simplified implementation and also offers a simple decomposition of the problem into clearly identifiable subproblems. The node-tearing ordering heuristic has proven to be successful in identifying the hierarchical structure in the power systems matrices, and reducing the number of coupling equations so that the graph multi-coloring algorithm can usually color the last block with only two or three colors. All available parallelism in our Gauss-Seidel algorithm is derived from within the actual interconnection relationships between elements in the matrix, and identified in the sparse matrix orderings. Consequently, available parallelism is not unlimited. Relative speedup tends to increase nicely until either load-balance overhead or communications overhead cause speedup to level off.

We have shown that, depending on the matrix, relative efficiency declines rapidly after 8 or 16 processors, limiting the utility of applying large numbers of processors to a single parallel linear solver. Nevertheless, other dimensions exist in electrical power system applications that can be exploited to use large numbers of processors efficiently. While a moderate number of processors can be efficiently applied to a single power system simulation, multiple events can be simulated simultaneously.





David P. Koester
Sun Oct 22 15:29:26 EDT 1995