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For parallel sparse block-diagonal-bordered direct linear solvers to
be efficient when factoring irregular sparse matrices, the following
three step preprocessing phase is required:
- order the matrix into block-diagonal-bordered form while minimizing the number of calculations,
- pseudo-factor the matrix to identify both fillin and the number of calculations for all diagonal blocks and corresponding portions of the borders,
- load balance the matrix to distribute the calculations uniformly among processors.
The first step determines the block-diagonal-bordered form and the
ordering of nodes within diagonal blocks to minimize calculations; the
second step determines the locations of fillin values for static data
structures and also determines the number of calculations in
independent blocks for the load balancing step; and the third step
determines a mapping of data to processors for efficient
implementation of the algorithm for the user specified data.
David P. Koester
Sun Oct 22 17:27:14 EDT 1995