An efficient implementation of certain iterative refinement preconditioners
type: Item
instance of: scholarly article
title: An efficient implementation of certain iterative refinement preconditioners
zbMATH Open document ID: 0797.65027
DOI: 10.1007/BF02243396
published in: Computing
publication date: 1994-10-09T00:00:00Z
review text: The BEPS preconditioner cf. \textit{J. H. Bramble, R. E. Ewing, J. E. Pasciak} and \textit{A. H. Schatz} [Comput. Methods Appl. Mech. Eng. 67, No. 2, 149-159 (1988; Zbl 0632.76112)] was suggested to solve linear systems arising from the discretization of elliptic or parabolic problems on grids with local refinement. This paper is concerned with an efficient implementation of the BEPS preconditioner for the preconditioned conjugate gradient (CG) method or in the case of unsymmetric system matrices for the preconditioned variants of the generalized conjugate gradient -- least squares (GCG-LS) or the generalized minimal residual (GMRES) methods. The efficient implementation is based on exploiting the sparsity pattern of residuals with nonzero entries appearing only on the interface between the coarse grid and the local fine grid.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65N22
zbMATH DE Number: 519761
zbMATH Keywords: local grid refinement
zbMATH Keywords: preconditioned conjugate gradient method
zbMATH Keywords: generalized minimal residual methods
zbMATH Keywords: least squares method
zbMATH Keywords: BEPS preconditioner
zbMATH Keywords: sparsity pattern of residuals
author: S. I. Petrova
reviewed by: R. Blaheta
describes a project that uses: CGS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 519761