An incomplete factorization preconditioning method based on modification of element matrices
type: Item
instance of: scholarly article
title: An incomplete factorization preconditioning method based on modification of element matrices
zbMATH Open document ID: 0859.65029
DOI: 10.1007/BF01740546
author: Ivar Gustafsson
published in: BIT
publication date: 1997-04-07T00:00:00Z
review text: The paper concerns the problem of stability of incomplete factorization (IC) and modified incomplete factorization (MIC) of matrices arising from the finite element solution of selfadjoint boundary value problems. For the purpose of construction of a stable incomplete factorization, it introduces an auxiliary matrix arising from the assembly of modified element matrices. This matrix is a weakly diagonally dominant \(M\)-matrix and can therefore be exploited for the construction of IC or MIC preconditioners. Moreover, this auxiliary matrix is spectrally equivalent to the original finite element matrix so that the asymptotic effect of preconditioning is preserved. The author applies the above idea to several cases of higher-order elements, hierarchical elements and anisotropy problems and shows favourable behaviour of the introduced technique.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 881185
zbMATH Keywords: incomplete factorization preconditioning method
zbMATH Keywords: stability
zbMATH Keywords: finite element
zbMATH Keywords: weakly diagonally dominant \(M\)-matrix
zbMATH Keywords: preconditioners
reviewed by: R. Blaheta
describes a project that uses: DRIC
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 881185