Recursive two-level ILU preconditioner for nonsymmetric M-matrices
type: Item
instance of: scholarly article
title: Recursive two-level ILU preconditioner for nonsymmetric M-matrices
zbMATH Open document ID: 1069.65027
DOI: 10.1007/BF02936148
author: Yanyan Li
published in: Journal of Applied Mathematics and Computing
publication date: 2004-10-28T00:00:00Z
review text: The authors start from a block-LU decomposition of \(A\) (which is a \(2\times 2\) block matrix, possibly approximating a partial differential equation on two grids or on one grid with an ordering of the points into fine and coarse ones) and approximate this LU decomposition by approximating the pivot block, its inverse (for use in an approximate Schur complement \(S\)) and by possibly skipping off-diagonal elements of \(S\). They show for M-matrices \(A\) [referring often to \textit{O. Axelsson}'s book: Iterative solution methods (1994; Zbl 0795.65014)] that this scheme works recursively (after \(A\), \(S\) is \(2\times 2\) block decomposed etc.) under appropriate conditions on the approximations. The English of the paper is curious at places but the authors make a good job in presenting 3 diagonal approximations of the inverse of the pivot which are easy to compute and satisfy the conditions. Numerical results are reasonable and concern 2D convection diffusion problems approximated by an upwind difference scheme.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 2111237
zbMATH Keywords: sparse M-matrices
zbMATH Keywords: preconditioning
zbMATH Keywords: block LU factorization
zbMATH Keywords: Schur complement
zbMATH Keywords: convection-diffusion equations
zbMATH Keywords: numerical results
zbMATH Keywords: upwind difference scheme
describes a project that uses: ILUM
describes a project that uses: BILUTM
describes a project that uses: SPARSKIT
describes a project that uses: ILUT
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2111237