LU Factorization of Sparse, Unsymmetric Jacobian Matrices on Multicomputers: Experience, Strategies, Performance
- Creators
- Skjellum, Anthony
- Leung, Alvin P.
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.
Additional Information
© 1990 IEEE. The authors acknowledge Prof. Manfred Morari, who supervised the work presented in this student paper. We wish to acknowledge the dense concurrent linear algebra library provided by Eric Van de Velde, as well as a prototype sparse concurrent linear algebra library, both of which were useful springboards for this work. The first author acknowledges partial support under DOE grants DE-FG03-85ER25009 and DEACOS-85ER40050. The second author (presently at the University of California, Santa Cruz) received support for his 1989 Caltech Summer Undergraduate Research Fellowship (SURF) under the same grants, and wishes to thank the Caltech SURF program for the opportunity to pursue the research discussed in part here. The software implementation of this research was accomplished using machine resources made available by the Caltech Computer Science sub-Micron System Architectures Project and the Caltech Concurrent Supercomputer hcilities (CCSF).Attached Files
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Additional details
- Eprint ID
- 78581
- Resolver ID
- CaltechAUTHORS:20170626-162309323
- DE-FG03-85ER25009
- Department of Energy (DOE)
- DE-AC03-85ER40050
- Department of Energy (DOE)
- Caltech Summer Undergraduate Research Fellowship (SURF)
- Created
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2017-06-27Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field