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International Conference on High-Performance Computing and Networking

HPCN-Europe 2000: High Performance Computing and Networking pp 109–118Cite as

Towards an Implementation of a Multilevel ILU Preconditioner on Shared-Memory Computers

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1823))

Abstract

Recently, substantial progress has been made in the development of multilevel ILU-factorizations. These methods are attractive for very large problems due to their good convergence properties. We consider the parallelization of the instance MRILU, where we restrict to a version intended for scalar problems. The most time consuming parts in using MRILU are repeated multiplication of two sparse matrices in the construction phase and the multiplication of a sparse matrix and a full vector in the solution phase. Algorithms for these operations, as well as matrix transposition, are presented and have been tested on a Cray J90.

This research has been supported by the Stichting Nationale Computerfaciliteiten (National Computing Facilities Foundation, NCF).

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References

  1. R.E. Bank and C. Wagner. Multilevel ILU decomposition. Numer. Math., 82:543–576, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  2. E.F.F. Botta, K. Dekker, Y. Notay, A. van der Ploeg, C. Vuik, F.W. Wubs, and P.M. de Zeeuw. How fast the Laplace equation was solved in 1995. Appl. Numer. Math., 24:439–455, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  3. E.F.F. Botta and F.W. Wubs. Matrix Renumbering ILU: An effective algebraic multilevel ILU-preconditioner for sparse matrices. SIAM J. Matrix Anal. Appl., 20(4):1007–1026, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  4. E.F.F. Botta, F.W. Wubs, and A. van der Ploeg. A fast linear-system solver for large unstructured problems on a shared-memory computer. In O. Axelsson and B. Polman, editors, Proceedings of the Conference on Algebraic Multilevel Iteration Methods with Applications, pages 105–116, Nijmegen, The Netherlands, 1996. University of Nijmegen.

    Google Scholar 

  5. M.T. Jones and P.E. Plassman. A parallel coloring heuristic. SIAM J. Sci. Comput., 14(3):654–669, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Luby. A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput., 4:1036–1053, 1986.

    Article  MathSciNet  Google Scholar 

  7. A. Reusken. On a robust multigrid solver. Computing, 56(3):303, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  8. Y. Saad. ILUM: A multi-elimination ILU preconditioner for general sparse matrices. SIAM J. Sci. Comput., 17(4):830–847, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  9. Y. Saad. Iterative Methods for Sparse Linear Systems. PWS, 1996.

    Google Scholar 

  10. Y. Saad and J. Zhang. BILUM: Block versions of multi-elimination and multilevel ILU preconditioner for general sparse linear systems. Technical Report UMSI 97-126, University of Minnesota, Minneapolis, 1997.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computing Centre of the University of Groningen, Groningen

    Arnold Meijster

  2. Research Institute of Mathematics and Computer Science, P.O. Box 800, 9700 AV, Groningen, The Netherlands

    Fred Wubs

Authors
  1. Arnold Meijster
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  2. Fred Wubs
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Editor information

Editors and Affiliations

  1. Institute of Computer Science and Academic Computer Center CYFRONET, University of Mining and Metallurgy (AGH), al. Mickiewicza 30, 30-059, Cracow, Poland

    Marian Bubak

  2. Faculteit der Natuurwetenschappen, Wiskunde en Informatica, Universiteit van Amsterdam, 1098 SJ, Amsterdam, The Netherlands

    Hamideh Afsarmanesh  & Bob Hertzberger  & 

  3. California Institute of Technology, Caltech 158-79, Pasadena, CA, 91125, USA

    Roy Williams

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© 2000 Springer-Verlag Berlin Heidelberg

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Meijster, A., Wubs, F. (2000). Towards an Implementation of a Multilevel ILU Preconditioner on Shared-Memory Computers. In: Bubak, M., Afsarmanesh, H., Hertzberger, B., Williams, R. (eds) High Performance Computing and Networking. HPCN-Europe 2000. Lecture Notes in Computer Science, vol 1823. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45492-6_12

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  • DOI: https://doi.org/10.1007/3-540-45492-6_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67553-2

  • Online ISBN: 978-3-540-45492-2

  • eBook Packages: Springer Book Archive

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