A direct Schur-Fourier decomposition for the efficient solution of high-order Poisson equations on loosely coupled parallel computers

摘要

In this paper a parallel direct Schur-Fourier decomposition (DSFD) algorithm for the direct solution of arbitrary order discrete Poisson equations on parallel computers is proposed. It is based on a combination of a Direct Schur method and a Fourier decomposition and allows to solve each Poisson equation almost to machine accuracy using only one communication episode. Thus, it is well suited for loosely Coupled parallel computers, that have a high network latency compared with the CPU performance. Several three-dimensional direct numerical simulations (DNS) of wall-bounded turbulent incompressible flows have been carried out using the DSFD algorithm. Numerical examples illustrating the robustness and scalability of the method on a PC cluster with a conventional 100 Mbits/s network are also presented. Copyright (C) 2005 John Wiley & Sons, Ltd.