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Parallel multilevel algorithms for solving the incompressible Navier-Stokes equations. (English) Zbl 0989.76041

Krause, Egon (ed.) et al., High performance computing in science and engineering ’98. Transactions of the High Performance Computing Center Stuttgart (HLRS) 1998. 1st workshop, Stuttgart, Germany, June 22-24, 1998. Berlin: Springer. 308-325 (1999).
Summary: This paper presents results of a numerical study for unsteady three-dimensional, incompressible flow. A finite element multigrid method is used in combination with 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/pressure, is used for spatial discretization. The second-order fractional-step-\(\theta\)-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 are considered as stand-alone iterations. We present a very efficient implementation of Gauß-Seidel respectively 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 lengths. The measured performances are between 20 MFLOP for large vector length and 450 MFLOP for short vector length.
For the entire collection see [Zbl 0908.00025].

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65Y05 Parallel numerical computation
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