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Parallel multigrid algorithms for some specialized computer systems

  • Algorithmic Studies For Hypercube-Type Systems
  • Conference paper
  • First Online:
CONPAR 90 — VAPP IV (VAPP 1990, CONPAR 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 457))

Abstract

The paper deals with parallelization of multigrid algorithms for some specialized parallel computer systems. These algorithms are optimal because the number of operations that have to be performed linearly depends on the number of discrete unknowns which are to be evaluated. It is shown that for a SIMD-type computer the separate location of grid point values in orthogonal memory blocks and permutation network functions allow to implement the computational phases of the multigrid cycle in parallel. The effective mapping of partitioned grid onto the processors by the Gray code is described for hypercube multiprocessors. Finally, the VLSI design for a multigrid algorithm is presented where the best hitherto known upper bound for solving the model elliptic problem in the area-time complexity is achieved.

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References

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Authors and Affiliations

  1. Institute of Technical Cybernetics, Slovak Academy of Sciences, 842 37, Bratislava, Czechoslovakia

    Marián Vajteršic

Authors
  1. Marián Vajteršic
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Editor information

Helmar Burkhart

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© 1990 Springer-Verlag Berlin Heidelberg

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Vajteršic, M. (1990). Parallel multigrid algorithms for some specialized computer systems. In: Burkhart, H. (eds) CONPAR 90 — VAPP IV. VAPP CONPAR 1990 1990. Lecture Notes in Computer Science, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53065-7_163

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  • DOI: https://doi.org/10.1007/3-540-53065-7_163

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53065-7

  • Online ISBN: 978-3-540-46597-3

  • eBook Packages: Springer Book Archive

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