Adaptive algebraic smoothers
type: Item
instance of: scholarly article
title: Adaptive algebraic smoothers
zbMATH Open document ID: 1244.65048
author: B. Philip
author: Timothy P. Chartier
published in: Journal of Computational and Applied Mathematics
publication date: 2012-03-19T00:00:00Z
review text: Construction of smoothers which are appropriate for a certain problem is a cumbersome task. This paper attempts to automate the process of smoother construction using \textit{local sensitivity analysis} (LSA). A measure based on LSA is introduced as a means of identifying strong coupling between variables. The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coefficient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system of partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem. Furthermore, it is possible to adaptively vary the size and strength of the blocks leading to the construction of a one parameter family of block iterative methods which can be tuned for a problem based on efficiency or convergence criteria.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 6015744
zbMATH Keywords: adaptive smoothers
zbMATH Keywords: block smoothers
zbMATH Keywords: line smoothers
zbMATH Keywords: multigrid
zbMATH Keywords: algebraic multigrid
zbMATH Keywords: local sensitivity analysis
zbMATH Keywords: Krylov method
zbMATH Keywords: preconditioners
zbMATH Keywords: block iterative method
zbMATH Keywords: convergence
describes a project that uses: ARMS
MaRDI profile type: Publication
full work available at URL: j.cam.2011.11.016
OpenAlex ID: W2013379422
Wikidata QID: Q57707675
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DBLP publication ID: journals/jcam/PhilipC12
DOI: 10.1016/J.CAM.2011.11.016
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description: scientific article; zbMATH DE number 6015744