Rigorous convergence proof of space-time multigrid with coarsening in space
type: Item
instance of: scholarly article
title: Rigorous convergence proof of space-time multigrid with coarsening in space
zbMATH Open document ID: 1489.65123
published in: Numerical Algorithms
publication date: 2022-01-13T00:00:00Z
full work available at URL: spacetimemg post.pdf
review text: The author presents a full convergence proof of space-time multigrid with coarsening in space, considering two families of smoothers that are well adapted to parallel computation. For waveform type smoothers, it is proved that the convergence can be uniform with respect to both the time step size and the mesh size. Such convergence result is not straightforward. It is also shown that time-parallel smoothers perform as well as waveform type smoother as long as the ratio \(\eta\) between the square mesh size and the time step size is below some threshold. Some numerical tests are presented to show the accuracy of the theoretical estimates.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 7456992
zbMATH Keywords: multigrid
zbMATH Keywords: linear systems
zbMATH Keywords: convergence analysis
zbMATH Keywords: discretized PDEs
zbMATH Keywords: parallel-in-time
author: Yvan Notay
describes a project that uses: MGRIT
MaRDI profile type: Publication
OpenAlex ID: W3172389476
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DOI: 10.1007/S11075-021-01129-2
description: scientific article; zbMATH DE number 7456992