Preconditioning of elliptic problems by approximation in the transform domain
type: Item
instance of: scholarly article
title: Preconditioning of elliptic problems by approximation in the transform domain
zbMATH Open document ID: 0890.65042
DOI: 10.1007/BF02510358
published in: BIT
publication date: 1998-07-06T00:00:00Z
review text: The numerical solution of second-order elliptic boundary value problems is examined. Using finite differences or finite elements, such problems generally are reduced to linear systems of the form \(Ax=b\), where \(A\) is a symmetric and positive definite sparse matrix. The author views the matrix \(A\) as an image and constructs the transform based preconditioner by using the low frequency components of the transformed matrix. The smooth coefficients of the given elliptic operator can be approximated well by the low-rank matrix. Numerical results are reported to show the effectiveness of the methodology.
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 1117814
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: transform approximation
zbMATH Keywords: numerical results
zbMATH Keywords: second-order elliptic boundary value problems
zbMATH Keywords: finite differences
zbMATH Keywords: finite elements
zbMATH Keywords: sparse matrix
zbMATH Keywords: preconditioner
author: Michael Ng
reviewed by: F. Szidarovszky
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02510358
OpenAlex ID: W2024670688
description: scientific article; zbMATH DE number 1117814