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Parallel multilevel algorithms for solving the incompressible Navier-Stokes equations

In: High Performance Computing in Science and Engineering ’98

Author

Listed:
  • Christian Becker

    (Universität Heidelberg, Institut für Angewandte Mathematik)

  • Hubertus Oswald

    (Universität Heidelberg, Institut für Angewandte Mathematik)

  • Stefan Turek

    (Universität Heidelberg, Institut für Angewandte Mathematik)

Abstract

This paper presents results of a numerical study for unsteady three—dimensional, incompressible flow. A finite element multigrid method is used in combination with an operator splitting technique and upwind discretization for the convective term. A nonconforming element pair, living on hexahedrons, which is of order O(h 2 /h) for velocity and pressure, is used for the spatial discretization. The second order fractional—step—θ—scheme is employed for the time discretization. For this approach we present the parallel implementation of a multigrid code for MIMD computers with message passing and distributed memory. Multiplicative multigrid methods as stand alone iterations are considered. We present a very efficient implementation of Gauß-Seidel resp. SOR smoothers, which have the same amount of communication as a Jacobi smoother. As well we present measured MFLOP for Blas 1 and Lin routines (as SAXPY) for different vector length. The measured performance are between 20 MFLOP for large vectorlength and 450 MFLOP for short vectorlength.

Suggested Citation

  • Christian Becker & Hubertus Oswald & Stefan Turek, 1999. "Parallel multilevel algorithms for solving the incompressible Navier-Stokes equations," Springer Books, in: Egon Krause & Willi Jäger (ed.), High Performance Computing in Science and Engineering ’98, pages 308-325, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-58600-2_30
    DOI: 10.1007/978-3-642-58600-2_30
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