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Sparse Matrix Solver Implementations

Implementations of a block-diagonal-bordered sparse LU solver and a similar Choleski solver have been developed in the C programming language for the Thinking Machines CM-5 multi-computer using message passing and a host-node paradigm. A version of the software is available that runs on a single processor on the CM-5 to provide empirical speed-up data to quantify multi-processor performance. Empirical performance data has been gathered for a range of numbers of processors and real power systems sparse network matrices. Results based on empirical data collected in benchmarking trials are presented in the next section. Our block-diagonal-bordered sparse solvers have the following distinct sections where blocks are defined in section 4:

  1. LU factorization
  2. forward reduction
  3. backward substitution
The Choleski factorization algorithm is similar to LU factorization, with the block-diagonal-bordered Choleski algorithm having the same distinct sections as described above with the exception of and being substituted for and respectively.

The parallel implementation presented in this section has been developed as an instrumented proof-of-concept to examine the efficiency of each section of the code described above. The host processor is used to gather and tabulate statistics on the multi-processor calculations. Statistics are gathered in a manner that do not impact the total empirical measures of performance for factorization, forward reduction, or backward substitution.





next up previous contents
Next: The Hierarchical Data Up: Parallel Direct Methods for Previous: The Node-tearing Implementation



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