Space-time domain decomposition for parabolic problems
type: Item
instance of: scholarly article
title: Space-time domain decomposition for parabolic problems
zbMATH Open document ID: 1019.65076
author: Eldar Giladi
author: Herbert B. Keller
published in: Numerische Mathematik
publication date: 2003-03-18T00:00:00Z
review text: This paper concerns a space-time domain decomposition iteration for a model advection diffusion equation in one and two dimensions. The discretization of this iteration is the block red-black variant of the waveform relaxation method and some new convergence results for this scheme are obtained. The asymptotic convergence rate is superlinear and is governed by the diffusion of the error across the overlap between subdomains. It depends on the size of this overlap and the diffusion coefficient in the equation. The convergence rate for the heat equation in a large time window is initially linear and it deteriorates as the number of subdomains increases. The duration of the transient linear regime is propositional to the length of the time window. For advection dominated problems, the convergence rate is initially linear and it improves as the ratio of advection to diffusion increases. It is independent of the size of the time window and of the number of subdomains. Numerical examples are given.
Mathematics Subject Classification ID: 65M55
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 1884035
zbMATH Keywords: numerical examples
zbMATH Keywords: space-time domain decomposition
zbMATH Keywords: advection diffusion equation
zbMATH Keywords: waveform relaxation method
zbMATH Keywords: convergence
zbMATH Keywords: heat equation
reviewed by: Laura Iulia Aniţa
MaRDI profile type: Publication
full work available at URL: s002110100345
OpenAlex ID: W1998789711
DOI: 10.1007/S002110100345
description: scientific article; zbMATH DE number 1884035