On the efficiency of a SOR-like method suited to vector processors
type: Item
instance of: scholarly article
title: On the efficiency of a SOR-like method suited to vector processors
zbMATH Open document ID: 0729.65022
DOI: 10.1016/0377-0427(91)90196-Q
author: Masaaki Sugihara
author: Yoshio Oyanagi
author: Masatake Mori
author: Seiji Fujino
published in: Journal of Computational and Applied Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Consider the Poisson equation on the unit square, with the five point discretization. In the rowwise left to right and upwards ordering of the nodes, the successive overrelaxation (SOR) method uses the western and southern updates from the current iteration and the northern and eastern ones from the preceding iteration. The SOR-like method uses the new southern updates and the old ones for the remaining directions. This method has the advantage of being easily vectorizable with constant vector length, in opposition to the hyperplane version of SOR. On the other hand, the convergence rate of SOR is better by an order of magnitude. The authors also discuss the nine point discretization. They finally present a careful set of experiments carried on several powerful supercomputers. These experiments show that vectorized SOR, based on the hyperplane version, is always faster than vectorized SOR-like.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 4205866
zbMATH Keywords: vector computers
zbMATH Keywords: hyperplane method
zbMATH Keywords: Poisson equation
zbMATH Keywords: five point discretization
zbMATH Keywords: successive overrelaxation
zbMATH Keywords: convergence rate
zbMATH Keywords: nine point discretization
zbMATH Keywords: supercomputers
reviewed by: Juan Pedro Milaszewicz
MaRDI profile type: Publication
cites work: Q3293417
cites work: The parallel execution of DO loops
cites work: Q3993065
cites work: Application of variational methods in the fixed and adaptive grid generation
cites work: Q5342712
full work available at URL: 0377-0427(91)90196-q
OpenAlex ID: W2069263871
description: scientific article; zbMATH DE number 4205866