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Empirical Results for Parallel Direct Linear Solvers

A stated goal of this block-diagonal-bordered direct solver is to simplify the task organization of the parallel LU algorithm and have interprocessor communications significantly reduced and regular. The performance of this block-diagonal-bordered LU solver is dependent on the ability to order the real power systems sparse matrices into the desired form with uniformly distributed data in the diagonal blocks and a minimum number of equations in the lower border.

In section 7.1.1, we illustrate the ordering capabilities of the node-tearing nodal analysis by presenting pseudo-images of selected sparse power systems network matrices after we have applied both our node-tearing algorithm to partition the matrices into block-diagonal-bordered form and our pigeon-hole load-balancing algorithm. We provide additional information as to the overall performance of the three-step preprocessing phase, with special note to the amount of fillin in the matrices after ordering and to the total number of floating point operations required to factor the matrices. We then report on the performance of the block-diagonal-bordered sparse LU and Choleski solvers in section 7.1.2. Performance of these parallel block-diagonal-bordered direct linear solvers is dependent upon the ability of the preprocessing phase, in addition to the performance of the parallel implementations. The real performance test of the node-tearing algorithm occurs when the performance of the block-diagonal-bordered sparse LU solver is examined for real power system network matrices in section 7.1.2. In section 7.1.3, we compare the performance of low-latency, active message-based implementations and buffered communications-based implementations. In section 7.1.4, we present preliminary results when running the complex variate LU algorithms on the IBM SP1 and SP2 scalable parallel processors, and in section 7.1.5, we present our conclusions concerning the performance of our parallel direct implementations.





David P. Koester
Sun Oct 22 17:27:14 EDT 1995