'Institute of Electrical and Electronics Engineers (IEEE)'
Abstract
Efficient sparse linear algebra cannot be achieved as
a straightforward extension of the dense case, 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
