On the convergence rate of a space decomposition method
type: Item
instance of: scholarly article
title: On the convergence rate of a space decomposition method
zbMATH Open document ID: 1024.65048
author: Guihua Shan
author: Shuzi Zhou
author: Jinping Zeng
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2003-11-06T00:00:00Z
review text: An abstract minimization problem for a \(C^2\)-functional \(F:V\to{\mathbb R}\) whose derivative \(F'\) is Lipschitz continuous and uniformly monotone on each bounded set of a reflexive Banach space \(V\) is considered. A space-decomposition method, relying on a decomposition \(V=V_1+\cdots +V_m\), is scrutinized in connection with the iterative minimization algorithm making partial minimizations on each subspaces \(V_1\), \dots , \(V_m\) whose minimizers are further used to determine a direction for a line-search step to up-date the current iteration. The rate of convergence is proved. It is mentioned that it is a unified framework for both domain decomposition method and multigrid method used in numerical solutions of boundary-value problems for elliptic partial differential equations.
reviewed by: Tomáş Roubíçek
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 49M27
zbMATH DE Number: 1885787
zbMATH Keywords: minimization on a Banach space
zbMATH Keywords: Schwarz iterative algorithms
zbMATH Keywords: geometric convergence
zbMATH Keywords: domain decomposition method
zbMATH Keywords: multigrid method
zbMATH Keywords: algorithm
zbMATH Keywords: boundary-value problems
zbMATH Keywords: elliptic partial differential equations
MaRDI profile type: Publication
full work available at URL: s102550200045
OpenAlex ID: W2014645598
cites work: Q4272015
cites work: Q3806726
cites work: Rate of Convergence of Some Space Decomposition Methods for Linear and Nonlinear Problems
cites work: Iterative Methods by Space Decomposition and Subspace Correction
cites work: Some Nonoverlapping Domain Decomposition Methods
cites work: On Monotone and Geometric Convergence of Schwarz Methods for Two-Sided Obstacle Problems
cites work: Q3747633
DOI: 10.1007/S102550200045
description: scientific article; zbMATH DE number 1885787