Convergence of the parallel chaotic waveform relaxation method for stiff systems
type: Item
instance of: scholarly article
title: Convergence of the parallel chaotic waveform relaxation method for stiff systems
zbMATH Open document ID: 1016.65058
DOI: 10.1016/S0377-0427(02)00749-5
author: Dongjin Yuan
author: Kevin Burrage
published in: Journal of Computational and Applied Mathematics
publication date: 2003-03-16T00:00:00Z
review text: Ideas for the numerical solution of stiff linear systems of ordinary differential equations are presented, where the dimension is assumed to be very large. Specifically the authors propose to use the waveform relaxation technique to decompose the full system into smaller subsystems. On a parallel computer, each subsystem is then solved on its own processor. The computation is performed in an asynchronous way, so each processor can work independently of the others. Three different concrete realizations of this concept are introduced and analyzed with respect to their convergence behaviour: A fundamental asynchronous parallel multisplitting scheme, a relaxed variant of this, and a more complex overlapping multisplitting method. Numerical examples are given.
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 1882248
zbMATH Keywords: multisplitting
zbMATH Keywords: waveform relaxation
zbMATH Keywords: stiff systems
zbMATH Keywords: parallel algorithm
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
cites work: Q3943082
cites work: Q4001523
cites work: Models of parallel chaotic iteration methods
cites work: Q4846444
cites work: On the performance of parallel waveform relaxations for differential systems
cites work: Chaotic relaxation
cites work: Convergence of Waveform Relaxation Methods for Differential-Algebraic Systems
cites work: Multigrid Waveform Relaxation of Spatial Finite Element Meshes: The Continuous-Time Case
cites work: Waveform Relaxation with Overlapping Splittings
cites work: A note on convergence conditions of waveform relaxation algorithms for nonlinear differential-algebraic equations
cites work: Convergence of relaxed chaotic parallel iterative methods
cites work: Convergence of Dynamic Iteration Methods for Initial Value Problems
cites work: Multi-Splittings of Matrices and Parallel Solution of Linear Systems
cites work: On the convergence of the discretized multi-splitting waveform relaxation algorithm
Recommended article: On the convergence of the discretized parallel chaotic waveform relaxation method.
Recommended article: Convergence of relaxed chaotic parallel iterative methods
Recommended article: On the convergence of waveform relaxation methods for stiff nonlinear ordinary differential equations
Recommended article: Chaotic waveform relaxation methods for dynamical systems
Recommended article: Q4271770
Recommended article: On the performance of parallel waveform relaxations for differential systems
Recommended article: Convergence of Waveform Relaxation Methods for Differential-Algebraic Systems
Recommended article: Q5386397
Recommended article: Convergence of relaxed matrix parallel multisplitting chaotic methods for \(H\)-matrices
Recommended article: Q4022269
description: scientific article; zbMATH DE number 1882248