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LU Factorization of Sparse, Unsymmetric Jacobian Matrices


Efficient sparse linear algebra cannot be achieved as a straightforward extension of the dense case described in Chapter 8, even for concurrent implementations. This paper details a new, general-purpose unsymmetric sparse LU factorization  code built on the philosophy of Harwell's MA28, with variations. We apply this code in the framework of Jacobian-matrix factorizations, arising from Newton iterations in the solution of nonlinear systems of equations. Serious attention has been paid to the data-structure requirements, complexity issues, and communication features of the algorithm. Key results include reduced communication pivoting  for both the ``analyze'' A-mode and repeated B-mode factorizations, and effective general-purpose data distributions useful incrementally to trade-off process-column load balance  in factorization against triangular solve performance. Future planned efforts are cited in conclusion.

Other References

HPFA Paradigms

Guy Robinson
Wed Mar 1 10:19:35 EST 1995