Skip to main content

A Shared- and Distributed-Memory Parallel Sparse Direct Solver

  • Conference paper
Applied Parallel Computing. State of the Art in Scientific Computing (PARA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3732))

Included in the following conference series:

  • 1237 Accesses

Abstract

In this paper, we describe a parallel direct solver for general sparse systems of linear equations that has recently been included in the Watson Sparse Matrix Package (WSMP) [7]. This solver utilizes both shared- and distributed- memory parallelism in the same program and is designed for a hierarchical parallel computer with network-interconnected SMP nodes. We compare the WSMP solver with two similar well known solvers: MUMPS [2] and Super_LU Dist  [10]. We show that the WSMP solver achieves significantly better performance than both these solvers based on traditional algorithms and is more numerically robust than Super_LU Dist . We had earlier shown [8] that MUMPS and Super_LU Dist are amongst the fastest distributed-memory general sparse solvers available.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Amestoy, P.R., Davis, T.A., Duff, I.S.: An approximate minimum degree ordering algorithm. SIAM Journal on Matrix Analysis and Applications 17(4), 886–905 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  • Amestoy, P.R., Duff, I.S., Koster, J., L’Excellent, J.Y.: A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM Journal on Matrix Analysis and Applications 23(1), 15–41 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Davis, T.A., Duff, I.S.: An unsymmetric-pattern multifrontal method for sparse LU factorization. SIAM Journal on Matrix Analysis and Applications 18(1), 140–158 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  • Duff, I.S., Koster, J.: On algorithms for permuting large entries to the diagonal of a sparse matrix. SIAM Journal on Matrix Analysis and Applications 22(4), 973–996 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Gupta, A.: A high-performance GEPP-based sparse solver. In: Proceedings of PARCO (2001), http://www.cs.umn.edu/~agupta/doc/parco-01.ps

  • Gupta, A.: Improved symbolic and numerical factorization algorithms for unsymmetric sparse matrices. SIAM Journal on Matrix Analysis and Applications 24(2), 529–552 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • Gupta, A.: WSMP: Watson sparse matrix package (Part-II: direct solution of general sparse systems). Technical Report RC 21888 (98472), IBM T. J. Watson Research Center, Yorktown Heights, NY, November 20 (2000), http://www.cs.umn.edu/~agupta/wsmp

  • Gupta, A.: Recent advances in direct methods for solving unsymmetric sparse systems of linear equations. ACM Transactions on Mathematical Software 28(3), 301–324 (2002)

    Article  MATH  Google Scholar 

  • Hadfield, S.M.: On the LU Factorization of Sequences of Identically Structured Sparse Matrices within a Distributed Memory Environment. PhD thesis, University of Florida, Gainsville, FL (1994)

    Google Scholar 

  • Li, X.S., Demmel, J.W.: SuperLU DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems. ACM Transactions on Mathematical Software 29(2), 110–140 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  • Schulze, J.: Towards a tighter coupling of bottom-up and top-down sparse matrix ordering methods. Bit Numerical Mathematics 41(4), 800–841 (2001)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gupta, A. (2006). A Shared- and Distributed-Memory Parallel Sparse Direct Solver. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_94

Download citation

  • DOI: https://doi.org/10.1007/11558958_94

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29067-4

  • Online ISBN: 978-3-540-33498-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics