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Parallel Pivots LU Algorithm on the Cray T3E

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Book cover Parallel Computation (ACPC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1557))

Abstract

Solving large nonsymmetric sparse linear systems on distributed memory multiprocessors is an active research area. We present a loop-level parallelized generic LU algorithm which comprises analysefactorize and solve stages. To further exploit matrix sparsity and parallelism, the analyse step looks for a set of compatible pivots. Sparse techniques are applied until the reduced submatrix reaches a threshold density. At this point, a switch to dense routines takes place in both analyse-factorize and solve stages. The SPMD code follows a sparse cyclic distribution to map the system matrix onto a P× Q processor mesh. Experimental results show a good behavior of our sequential algorithm compared with a standard generic solver: the MA48 routine. Additionally, a parallel version on the Cray T3E exhibits high performance in terms of speed-up and efficiency.

The work described in this paper was supported by the Ministry of Education and Science (CI-CYT) of Spain under project TIC96-1125-C03, by the European Union under contract BRITE-EURAM III BE95-1564, by the Human Capital and Mobility programme of the European Union under project ERB4050P1921660, and by the Training and Research on Advanced Computing Systems (TRACS) at the Edinburgh Parallel Computing Centre (EPCC)

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Authors and Affiliations

  1. Computer Architecture Department, University of Málaga, Spain

    Rafael Asenjo & Emilio L. Zapata

Authors
  1. Rafael Asenjo
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  2. Emilio L. Zapata
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Editors and Affiliations

  1. Forschungsinstitut für Softwaretechnologie, Hellbrunnerstr. 34, A-5020, Salzburg, Austria

    Peter Zinterhof

  2. Slovac Academy of Sciences, Institute of Mathematics, Laboratory for Informatics, Dubravska 9, P.O.Box 56, 840 00, Bratislava, Slovakia

    Marian Vajteršic

  3. Universität Salzburg, RIST++, Hellbrunnerstr. 34, A-5020, Salzburg, Austria

    Andreas Uhl

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© 1999 Springer-Verlag Berlin Heidelberg

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Asenjo, R., Zapata, E.L. (1999). Parallel Pivots LU Algorithm on the Cray T3E. In: Zinterhof, P., Vajteršic, M., Uhl, A. (eds) Parallel Computation. ACPC 1999. Lecture Notes in Computer Science, vol 1557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49164-3_4

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  • DOI: https://doi.org/10.1007/3-540-49164-3_4

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  • Print ISBN: 978-3-540-65641-8

  • Online ISBN: 978-3-540-49164-4

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