On preconditioning Schur complement and Schur complement preconditioning
type: Item
instance of: scholarly article
title: On preconditioning Schur complement and Schur complement preconditioning
zbMATH Open document ID: 0951.65042
author: Jun Zhang
publication date: 2000-07-24T00:00:00Z
full work available at URL: https://eudml.org/doc/120679
full work available at URL: pp115-130.html
review text: The author discusses implementation strategies of a class of multilevel recursive incomplete LU preconditioners. These preconditioners are based on block incomplete LU factorization of the coefficient matrix \(A\) of the linear system. To construct such an algorithm, a sparse matrix, based on an incomplete LU factorization of the matrix \(A\), is constructed as a preconditioner. In the preconditioning process, the Schur complement matrices are formed. Two implementation strategies are presented, both use the Schur complement matrix to precondition the matrix \(A\). The Schur complement preconditioning strategy seems to converge in a smaller number of iterations than the preconditioning Schur complement strategy does. Numerical experiments are performed (a convection-diffusion problem using standard 5-point central difference discretization scheme and a fourth-order 9-point compact finite difference discretization scheme).
reviewed by: Iulian Coroian
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 1476907
zbMATH Keywords: convergence
zbMATH Keywords: sparse matrices
zbMATH Keywords: Schur complement
zbMATH Keywords: multilevel incomplete LU factorization
zbMATH Keywords: preconditioning
zbMATH Keywords: algorithm
zbMATH Keywords: numerical experiments
zbMATH Keywords: convection-diffusion problem
zbMATH Keywords: finite difference discretization
describes a project that uses: BILUM
describes a project that uses: SparseMatrix
MaRDI profile type: Publication
published in: ETNA - Electronic Transactions on Numerical Analysis
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description: scientific article; zbMATH DE number 1476907