An almost optimal method for Dirichlet problems on decomposition subdomains of the hierarchical \(hp\)-version
type: Item
instance of: scholarly article
title: An almost optimal method for Dirichlet problems on decomposition subdomains of the hierarchical \(hp\)-version
zbMATH Open document ID: 1013.65135
DOI: 10.1023/A:1011970023932
author: V. Korneev
published in: Differential Equations
publication date: 2003-06-17T00:00:00Z
review text: The discrete Dirichlet problem arising in the domain decomposition method for the interior Dirichlet problems and the preconditioner suggested by \textit{V. G. Korneev} and \textit{S. A. Ivanov} [Mat. Model. 8, No.~9, 63--73 (1996; Zbl 0981.65512)] are considered. The preconditioner is interpretated as a finite-difference operator and is modified on the basis of decomposition of the domain. Exactly, the unit square is decomposed into rectangular subdomains in which the coefficients of the differential equation can be treated as constants without loss of the spectral equivalence. The main ingredients of the fast inversion method for the preconditioner are the fast discrete Fourier transform, the Thomas method for tridiagonal matrices, and the Cholesky elimination method. In the conclusion the total computational complexity of the numerical method is estimated.
reviewed by: Nikolai Pleshchinskii
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 1758776
zbMATH Keywords: domain decomposition method
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: preconditioner
zbMATH Keywords: finite-difference operator
zbMATH Keywords: fast inversion method
zbMATH Keywords: discrete Fourier transform
zbMATH Keywords: Cholesky elimination method
zbMATH Keywords: computational complexity
zbMATH Keywords: Thomas method
MaRDI profile type: Publication
full work available at URL: a:1011970023932
OpenAlex ID: W334763611
description: scientific article; zbMATH DE number 1758776