Premium
A direct Schur–Fourier decomposition for the efficient solution of high‐order Poisson equations on loosely coupled parallel computers
Author(s) -
Trias F. X.,
Soria M.,
PérezSegarra C. D.,
Oliva A.
Publication year - 2006
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.466
Subject(s) - robustness (evolution) , fast fourier transform , scalability , poisson's equation , domain decomposition methods , bounded function , poisson distribution , direct numerical simulation , computer science , parallel computing , fourier series , fourier transform , parallel algorithm , mathematics , compressibility , algorithm , computational science , mathematical analysis , turbulence , finite element method , physics , statistics , reynolds number , gene , thermodynamics , biochemistry , chemistry , database
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 © 2005 John Wiley & Sons, Ltd.