A parareal algorithm based on waveform relaxation
type: Item
instance of: scholarly article
title: A parareal algorithm based on waveform relaxation
zbMATH Open document ID: 1256.65071
author: Jun Liu
author: Yao-Lin Jiang
published in: Mathematics and Computers in Simulation
publication date: 2012-11-15T00:00:00Z
review text: Parareal algorithms are variants of multiple shooting methods and time-multigrid methods. The authors combine the known parareal and waveform relaxation (WR) techniques to develop a new parallel algorithm, which can be carried out in parallel in sub-systems and time. A sharp upper bound on errors is presented, which indicates the superlinear convergence of the algorithm. The performance of the new algorithm is optimized by balancing both methods. In addition, it is observed by numerical experiments that lower computational cost is needed than with the classical parareal algorithm to achieve the same accuracy. However, a future deferred correction strategy may promote the efficiency of the combination of the two different parallel approaches.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 6107084
zbMATH Keywords: parareal algorithm
zbMATH Keywords: waveform relaxation
zbMATH Keywords: parallelism in sub-systems and time
zbMATH Keywords: parallel computation
zbMATH Keywords: error bounds
zbMATH Keywords: multiple shooting methods
zbMATH Keywords: time-multigrid methods
zbMATH Keywords: superlinear convergence
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: j.matcom.2012.05.017
OpenAlex ID: W2050096672
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DOI: 10.1016/J.MATCOM.2012.05.017
description: scientific article; zbMATH DE number 6107084