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pARMS: A Package for Solving General Sparse Linear Systems on Parallel Computers

  • Y. Saad
  • M. Sosonkina
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2328)

Abstract

This paper presents an overview of pARMS, a package for solving sparse linear systems on parallel platforms. Preconditioners constitute the most important ingredient in the solution of linear systems arising from realistic scientific and engineering applications. The most common parallel preconditioners used for sparse linear systems adapt domain decomposition concepts to the more general framework of “distributed sparse linear systems”. The parallel Algebraic Recursive Multilevel Solver (pARMS) is a recently developed package which integrates together variants from both Schwarz procedures and Schur complement-type techniques. This paper discusses a few of the main ideas and design issues of the package. A few details on the implementation of pARMS are provided.

Keywords

Message Passing Interface Local Equation Sparse Linear System Local Matrix Interface Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    S. Balay, W. D. Gropp, L. Curfman McInnes, and B. F. Smith. PETSc 2.0 users manual. Technical Report ANL-95/11-Revision 2.0.24, Argonne National Laboratory, 1999.Google Scholar
  2. 2.
    V. Eijkhout and T. Chan. ParPre a parallel preconditioners package, reference manual for version 2.0.17. Technical Report CAM Report 97-24, UCLA, 1997.Google Scholar
  3. 3.
    W. Gropp, E. Lusk, and A. Skjellum. Using MPI: Portable Parallel Programming with the Message Passing Interface. MIT press, 1994.Google Scholar
  4. 4.
    Scott A. Hutchinson, John N. Shadid, and R. S. Tuminaro. Aztec user’s guide. version 1.0. Technical Report SAND95-1559, Sandia National Laboratories, Albuquerque, NM, 1995.Google Scholar
  5. 5.
    D. Hysom and A. Pothen. A scalable parallel algorithm for incomplete factor preconditioning. Technical Report (preprint), Old-Dominion University, Norfolk, VA, 2000.Google Scholar
  6. 6.
    M. T. Jones and P. E. Plassmann. BlockSolve95 users manual: Scalable library software for the solution of sparse linear systems. Technical Report ANL-95/48, Argonne National Lab., Argonne, IL., 1995.Google Scholar
  7. 7.
    Z. Li, Y. Saad, and M. Sosonkina. pARMS: a parallel version of the algebraic recursive multilevel solver. Technical Report umsi-2001-100, Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN, 2001.Google Scholar
  8. 8.
    G. Radicati di Brozolo and Y. Robert. Parallel conjugate gradient-like algorithms for solving sparse non-symmetric systems on a vector multiprocessor. Parallel Computing, 11:223–239, 1989.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Y. Saad. A flexible inner-outer preconditioned GMRES algorithm. SIAM J. on Sci. and Stat. Comput., 14:461–469, 1993.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Y. Saad. Krylov subspace methods in distributed computing environments. In M. Hafez, editor, State of the Art in CFD, pages 741–755, 1995.Google Scholar
  11. 11.
    Y. Saad. Iterative Methods for Sparse Linear Systems. PWS publishing, New York, 1996.zbMATHGoogle Scholar
  12. 12.
    Y. Saad and A. Malevsky. PSPARSLIB: A portable library of distributed memory sparse iterative solvers. In V. E. Malyshkin et al., editor, Proceedings of Parallel Computing Technologies (PaCT-95), 3-rd international conference, St. Petersburg, Russia, Sept. 1995, 1995.Google Scholar
  13. 13.
    Y. Saad and M. Sosonkina. Distributed schur complement techniques for general sparse linear systems. J. Scientific Computing, 21(4):1337–1356, 1999.MathSciNetCrossRefGoogle Scholar
  14. 14.
    Y. Saad and B. Suchomel. ARMS: An algebraic recursive multilevel solver for general sparse linear systems. Technical Report umsi-99-107-REVIS, Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN, 2001. Revised version of umsi-99-107.Google Scholar
  15. 15.
    Y. Saad and K. Wu. Parallel sparse matrix library (P_SPARSLIB): The iterative solvers module. Technical Report 94-008, Army High Performance Computing Research Center, Minneapolis, MN, 1994.Google Scholar
  16. 16.
    Y. Saad and K. Wu. Design of an iterative solution module for a parallel sparse matrix library (P_SPARSLIB). In W. Schonauer, editor, Proceedings of IMACS conference, Georgia, 1994, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Y. Saad
    • 1
  • M. Sosonkina
    • 2
  1. 1.University of MinnesotaMinneapolisUSA
  2. 2.University of MinnesotaDuluthUSA

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