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Modification of the ILU-Method for Enhanced Parallel Efficiency

  • Graham Horton
  • Ralf Knirsch
  • Gabriel Wittum
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)

Abstract

We consider the ILU method as an iteration for the solution of a two-dimensional p.d.e. when discretized on a regular square grid. It is known that a parallelization of this method is possible when the dimension of the processor array is less than that of the problem. However, in terms of parallelism, ILU methods suffer from two disadvantages: the procedure is not well vectorizable and it has a very fine granularity, making it unsuitable for some parallel architectures. In this presentation, two modifications to the method will be used to improve this state of affairs. A blocking method, which lumps communications together is used to coarsen the granularity. A modification to the computation of the which essentially removes the recursion is shown to enable both vectorization and a coarser granularity of parallelism. Experimental results demonstrate both the numerical behaviour of the schemes and the improvements in efficiency obtained on two DMMP parallel computers.

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References

  1. [l]
    P. Bastian, G. Horton : Parallelization of Robust Multi-Grid Methods: ILU Factorization and Frequency Decomposition Method. Proceedings of the Fifth GAMM Seminar, Kiel, 1989, Ed. W. Hackbusch and R. Rannacher, Vieweg Verlag, Braunschweig, 1990.Google Scholar
  2. [2]
    M. J. Flynn : Some Computer Organizations and their Effectiveness. IEEE Transactions on Computers, Vol. C-21, No. 9 (Sept. 1972).Google Scholar
  3. [3]
    W. Hackbusch : Iterative Lösung großer schwachbesetzter Gleichungssysteme. Teubner, Stuttgart, 1991.CrossRefzbMATHGoogle Scholar
  4. [4]
    P. Manneback, J. Qin, G. Libert : Performance Models of Modified Incomplete Cholesky Conjugate Gradient algorithm on Distributed Memory MIMD Computers. Proceedings of the European Workshop on Parallel Computing, Barcelona, March, 1992.Google Scholar
  5. [5]
    Meiko Scientific : Computing Surface User Manual ,Bristol 1990.Google Scholar
  6. [6]
    U. Trottenberg : Contributions of the 2nd International SUPRENUM Colloquium in Parallel Computing ,Parallel Computing 7, 1988.Google Scholar
  7. [7]
    G. Wittum : Linear iterations as smoothers in multigrid methods: Theory with applications to incomplete decompositions. Impact of Computing in Science and Engineering 1 , pp 180–215, 1989.CrossRefzbMATHGoogle Scholar
  8. [8]
    G. Wittum : Über spektralverschobene Iterationen. To appear.Google Scholar

Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1993

Authors and Affiliations

  • Graham Horton
    • 1
  • Ralf Knirsch
    • 1
  • Gabriel Wittum
    • 2
  1. 1.Lehrstuhl für Rechnerstrukturen (IMMD3)Universität Erlangen-NürnbergErlangenDeutschland
  2. 2.Institut für Angewandte MathematikUniversität HeidelbergHeidelbergDeutschland

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