A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations
type: Item
instance of: scholarly article
title: A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations
zbMATH Open document ID: 0829.65035
DOI: 10.1007/BF02521112
author: Rudnei Dias da Cunha
author: Tim Hopkins
published in: Advances in Computational Mathematics
publication date: 1996-01-25T00:00:00Z
review text: The authors present an algorithm of the restarted and preconditioned GMRES\((c)\) method with a restart \(c\). They describe the parallelisation of the GMRES\((c)\) and its implementation on distributed-memory architectures, using both networks of transputers and networks of workstations under the PVM message-passing system. The considered test systems of linear equations are derived from five-point finite difference approximations of convection-diffusion equations on the unit square. A theoretical model of the computation and communication phases is presented which allows us to describe for which values of the parameter \(c\) our implementation executes efficiently. The results show that for reasonably large discretisation grids the implementations are effective on a large number of processors.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 784496
zbMATH Keywords: parallel implementation
zbMATH Keywords: nonsymmetric system
zbMATH Keywords: preconditioning
zbMATH Keywords: GMRES\((c)\) method
zbMATH Keywords: restart
zbMATH Keywords: five-point finite difference approximations
zbMATH Keywords: convection- diffusion equations
reviewed by: Jan Zítko
describes a project that uses: PVM
describes a project that uses: PIM
MaRDI profile type: Publication
cites work: Q3139427
cites work: Parallel Triangular System Solving on a Mesh Network of Transputers
cites work: Q4296888
cites work: Approximating the inverse of a matrix for use in iterative algorithms on vector processors
cites work: Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
cites work: Q4880415
cites work: A data parallel finite element method for computational fluid dynamics on the Connection Machine system
cites work: Parallelizable restarted iterative methods for nonsymmetric linear systems. part I: Theory
cites work: Parallelizable restarted iterative methods for nonsymmetric linear systems. II: parallel implementation
cites work: Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: α-GMRES: A new parallelizable iterative solver for large sparse non-symmetric linear systems arising from CFD
cites work: Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
full work available at URL: https://doi.org/10.1007/bf02521112
OpenAlex ID: W2074605507
description: scientific article; zbMATH DE number 784496