Parallel multilevel algorithms for solving the incompressible Navier-Stokes equations

Christian Becker, Hubertus Oswald and Stefan Turek
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Christian Becker: Universität Heidelberg, Institut für Angewandte Mathematik
Hubertus Oswald: Universität Heidelberg, Institut für Angewandte Mathematik
Stefan Turek: Universität Heidelberg, Institut für Angewandte Mathematik

A chapter in High Performance Computing in Science and Engineering ’98, 1999, pp 308-325 from Springer

Abstract: 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.

Keywords: Lift Coefficient; Gaussian Elimination; Vector Length; Parallel Efficiency; Multigrid Algorithm (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-58600-2_30

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DOI: 10.1007/978-3-642-58600-2_30

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