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Parallelization of Multilevel ILU Preconditioners on Distributed-Memory Multiprocessors

  • José I. Aliaga
  • Matthias Bollhöfer
  • Alberto F. Martín
  • Enrique S. Quintana-Ortí
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7133)

Abstract

In this paper we investigate the parallelization of the ILUPACK library for the solution of sparse linear systems on distributed-memory multiprocessors. The parallelization approach employs multilevel graph partitioning algorithms in order to identify a set of concurrent tasks and their dependencies, which are then statically mapped to processors. Experimental results on a cluster of Intel QuadCore processors report remarkable speed-ups.

Keywords

Sparse linear system iterative solver preconditioner ILU decomposition MPI distributed-memory multiprocessor 

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References

  1. 1.
    Aliaga, J.I., Bollhöfer, M., Martín, A.F., Quintana-Ortí, E.S.: Parallelization of multilevel preconditioners constructed from inverse-based ILUs on shared-memory multiprocessors. In: Parallel Computing: Architectures, Algorithms and Applications. Advances in Parallel Computing, vol. 38, pp. 287–294. NIC (2007)Google Scholar
  2. 2.
    Aliaga, J.I., Bollhöfer, M., Martín, A.F., Quintana-Ortí, E.S.: Design, Tuning and Evaluation of Parallel Multilevel ILU Preconditioners. In: Palma, J.M.L.M., Amestoy, P.R., Daydé, M., Mattoso, M., Lopes, J.C. (eds.) VECPAR 2008. LNCS, vol. 5336, pp. 314–327. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Aliaga, J.I., Bollhöfer, M., Martín, A.F., Quintana-Ortí, E.S.: Exploiting thread-level parallelism in the iterative solution of sparse linear systems. Parallel Computing (2010) (in press, accepted manuscript) Google Scholar
  4. 4.
    Bollhöfer, M., Grote, M.J., Schenk, O.: Algebraic multilevel preconditioner for the helmholtz equation in heterogeneous media. SIAM Journal on Scientific Computing 31(5), 3781–3805 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bollhöfer, M., Saad, Y.: Multilevel preconditioners constructed from inverse–based ILUs. SIAM J. Sci. Comput. 27(5), 1627–1650 (2006); special issue on the 8–th Copper Mountain Conference on Iterative MethodsMathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chevalier, C., Pellegrini, F.: PT-SCOTCH: A tool for efficient parallel graph ordering. Parallel Comput. 34(6-8), 318–331 (2008)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Davis, T.A.: Direct Methods for Sparse Linear Systems. SIAM (2006)Google Scholar
  8. 8.
    Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359–392 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Karypis, G., Kumar, V.: A parallel algorithm for multilevel graph partitioning and sparse matrix ordering. J. Parallel Distrib. Comput. 48(1), 71–95 (1998)CrossRefGoogle Scholar
  10. 10.
    Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM Publications (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • José I. Aliaga
    • 1
  • Matthias Bollhöfer
    • 2
  • Alberto F. Martín
    • 1
  • Enrique S. Quintana-Ortí
    • 1
  1. 1.Dpto. de Ingen. y Ciencia de ComputadoresUniversidad Jaume ISpain
  2. 2.Institute of Computational MathematicsTU-BraunschweigGermany

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