Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing.
type: Item
instance of: scholarly article
title: Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing.
zbMATH Open document ID: 1289.65064
author: Petr Vaněk
author: Marian Brezina
published in: Applications of Mathematics
publication date: 2013-10-30T00:00:00Z
full work available at URL: http://hdl.handle.net/10338.dmlcz/143335
review text: The paper theoretically analyzes a general multigrid method in the case of the so called aggressive coarsening, i.e., with large differences between characteristic mesh sizes of two successive spaces within the multigrid hierarchy. The authors extend earlier theoretical results by weakening the approximation property and prove a ``nearly optimal convergence'' result independent of the coarsening ratio and linearly depending on the number of levels. Allowing worse approximation properties of the spaces requires to satisfy a stronger smoothing condition. A simple algorithm for the realisation of a suitable polynomial smoother based on Richardson iteration is described.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N55
zbMATH DE Number: 6221236
zbMATH Keywords: multigrid
zbMATH Keywords: aggressive coarsening
zbMATH Keywords: optimal convergence result
zbMATH Keywords: polynomial smoothing
zbMATH Keywords: algorithm
zbMATH Keywords: Richardson iteration
MaRDI profile type: Publication
OpenAlex ID: W1963871257
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DOI: 10.1007/S10492-013-0018-2
description: scientific article; zbMATH DE number 6221236