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LU Factorization of Sparse, Unsymmetric Jacobian Matrices on Multicomputers: Experience, Strategies, Performance

Skjellum, Anthony and Leung, Alvin P. (1990) LU Factorization of Sparse, Unsymmetric Jacobian Matrices on Multicomputers: Experience, Strategies, Performance. In: Proceedings of the Fifth Distributed Memory Computing Conference, 1990. IEEE , Piscataway, NJ, pp. 328-337. ISBN 0-8186-2113-3. https://resolver.caltech.edu/CaltechAUTHORS:20170626-162309323

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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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/DMCC.1990.555402DOIArticle
http://ieeexplore.ieee.org/document/555402/PublisherArticle
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).
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-85ER25009
Department of Energy (DOE)DE-AC03-85ER40050
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Record Number:CaltechAUTHORS:20170626-162309323
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170626-162309323
Official Citation:A. Skjellum and A. P. Leung, "LU Factorization of Sparse, Unsymmetric Jacobian Matrices on Multicomputers: Experience, Strategies, Performance," Proceedings of the Fifth Distributed Memory Computing Conference, 1990., 1990, pp. 328-337. doi: 10.1109/DMCC.1990.555402
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78581
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:27 Jun 2017 20:57
Last Modified:03 Oct 2019 18:09

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