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Empirical Results --- Conclusions

We have extensively analyzed the performance of parallel linear solvers for power systems applications on the Thinking Machines CM-5. We have shown that the performance of our parallel block-diagonal-bordered sparse linear solvers can yield good speedups for LU factorization. Power system matrices are so sparse that we were able to show that relative speedups for parallel Choleski factorization and complex-variate LU factorization can differ by factors from two to greater than three. There is a six-fold increase in the number of calculations for complex LU factorization versus Choleski factorization. The sparsity in the matrices has an even greater effect on the triangular solution steps as it does on the factorization. Communications overhead when reducing or substituting in the last diagonal block is so great that there is no available speedup, so the performance of these algorithms becomes limited by Amdahl's law for the Thinking Machines CM-5 architecture and software.





David P. Koester
Sun Oct 22 15:31:10 EDT 1995