Further comparison of additive and multiplicative coarse grid correction
type: Item
instance of: scholarly article
title: Further comparison of additive and multiplicative coarse grid correction
zbMATH Open document ID: 1271.65052
author: Artem Napov
author: Yvan Notay
published in: Applied Numerical Mathematics
publication date: 2013-02-21T00:00:00Z
full work available at URL: addmult.pdf
review text: A basic preconditioner is improved with a coarse grid correction and can be implemented either additively or multiplicatively like in the standard additive Schwarz method or in the balancing preconditioner, respectively. It is shown that the multiplicative variant has in fact always lower condition number when the basic preconditioner is appropriately scaled and assuming an appropriate scaling, the condition number of the additive variant is at worst a modest multiple of that of the multiplicative variant. Hence both approaches are qualitatively equivalent. Two examples show that both the upper and lower bounds on the condition number of the additive variant are sharp: it can be in some cases equal to the condition number of the multiplicative variant, and in other cases arbitrarily close to the aforementioned modest multiple of this latter value.
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 6138081
zbMATH Keywords: coarse grid correction
zbMATH Keywords: multigrid
zbMATH Keywords: domain decomposition
zbMATH Keywords: convergence
zbMATH Keywords: preconditioning
zbMATH Keywords: additive Schwarz method
zbMATH Keywords: scaling
zbMATH Keywords: condition number
MaRDI profile type: Publication
OpenAlex ID: W2048349268
DOI: 10.1016/J.APNUM.2012.12.001
description: scientific article; zbMATH DE number 6138081