On an energy minimizing basis for algebraic multigrid methods
type: Item
instance of: scholarly article
title: On an energy minimizing basis for algebraic multigrid methods
zbMATH Open document ID: 1077.65130
published in: Computing and Visualization in Science
publication date: 2005-06-14T00:00:00Z
review text: Energy minimal basis functions (EMBF) result in good multigrid convergence. EMBF and a numerical method for computing EMFB were first proposed by \textit{W. L. Wan, T. F. Chan}, and \textit{B. Smith} [SIAM J. Sci. Comput. 21, 1632--1649 (2000; Zbl 0966.65098)] but the numerical method is expensive. Smoothed aggregation constructs approximate EMBF, and a fast primal iterative method of projected gradient descent type to compute EMBF is obtained by more smoothing [cf. \textit{J. Mandel, M. Brezina}, and \textit{P. Vanek}, Computing 62, 205--228 (1999; Zbl 0942.65034)]. In this paper, a fast dual iterative method is proposed to compute EMBF. The new method is based on the inversion of an operator of abstract additive Schwarz type, which expresses the optimality condition of the energy in local subspaces. This leads to a well conditioned problem for the Lagrange multipliers. It is shown that the Lagrange multipliers are edge discrete harmonic and that EMBF are discrete harmonic on aggregated elements. There are numerical examples.
reviewed by: Jan Mandel
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 2175873
zbMATH Keywords: algebraic multigrid
zbMATH Keywords: iterative methods
zbMATH Keywords: adaptive methods
zbMATH Keywords: rough coefficients
zbMATH Keywords: discrete harmonic
zbMATH Keywords: energy minimal basis functions
zbMATH Keywords: convergence
zbMATH Keywords: Lagrange multipliers
zbMATH Keywords: numerical examples
author: Jinchao Xu
author: Ludmil T. Zikatanov
MaRDI profile type: Publication
full work available at URL: s00791-004-0147-y
OpenAlex ID: W1968536045
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DOI: 10.1007/S00791-004-0147-Y
description: scientific article; zbMATH DE number 2175873