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.

- 9.5.1 Introduction
- 9.5.2 Design Overview
- 9.5.3 Reduced-Communication Pivoting
- 9.5.4 New Data Distributions
- 9.5.5 Performance Versus Scattering
- 9.5.6 Performance
- 9.5.7 Conclusions

Other References

HPFA Paradigms

Wed Mar 1 10:19:35 EST 1995