Analyses of low-order preconditioners on high-order schemes for some model problems
type: Item
instance of: scholarly article
title: Analyses of low-order preconditioners on high-order schemes for some model problems
zbMATH Open document ID: 0765.65098
author: Weizhang Huang
published in: Chinese Science Bulletin
publication date: 1993-04-01T00:00:00Z
review text: The author considers the two- and the three-dimensional Poisson equation on the unit square and cube, respectively, with Dirichlet boundary condition. In order to efficiently solve the system of linear algebraic equations obtained by high-order discretization, a preconditioned conjugate gradient method is suggested where a preconditioner is constructed on the base of low order schemes for the same differential equation. Tables of difference schemes of order 2, 4, 6 and a comparison between the condition numbers of preconditioned matrices for higher and lower schemes are presented. Proofs and practical examples are missing, however, and from the text of the paper does not follow that the proposed procedures are better than other known methods.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 148457
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Poisson equation
zbMATH Keywords: preconditioned conjugate gradient method
zbMATH Keywords: difference schemes
zbMATH Keywords: comparison
zbMATH Keywords: condition numbers
reviewed by: Jan Zítko
MaRDI profile type: Publication
Recommended article: Analysis of a Semi-Circulant Preconditioner for a High-Order Compact Approximation of a Convection-Diffusion Model Problem
Recommended article: Low-Order Preconditioning for the High-Order Finite Element de Rham Complex
Recommended article: Analysis of Preconditioners for Hyperbolic Partial Differential Equations
Recommended article: Low-Order Preconditioning of High-Order Triangular Finite Elements
Recommended article: Analysis of Preconditioners for Domain Decomposition
Recommended article: An analysis of low-rank modifications of preconditioners for saddle point systems
Recommended article: Analysis of preconditioned iterative solvers for incompressible flow problems
Recommended article: Q3558545
Recommended article: Analysis of preconditioning strategies for collocation linear systems
Recommended article: Preconditioners for higher order finite element discretizations of \(H\)(div)-elliptic problem
description: scientific article; zbMATH DE number 148457