CONVERGENCE ANALYSIS OF INEXACT TWO-GRID METHODS: A THEORETICAL FRAMEWORK

doi:10.1137/20M1356075

	CONVERGENCE ANALYSIS OF INEXACT TWO-GRID METHODS: A THEORETICAL FRAMEWORK
	Xu, Xuefeng 1; Zhang, Chen-Song2,3,4
	2022
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	60 期号:1 页码:133-156
摘要	Multigrid is one of the most efficient methods for solving large-scale linear systems that arise from discretized partial differential equations. As a foundation for multigrid analysis, two-grid theory plays an important role in motivating and analyzing multigrid algorithms. For symmetric positive definite problems, the convergence theory of two-grid methods with exact solution of the Galerkin coarse-grid system is mature, and the convergence factor of exact two-grid methods can be characterized by an identity. Compared with the exact case, the convergence theory of inexact two-grid methods (i.e., the coarse-grid system is solved approximately) is of more practical significance, while it is still less developed in the literature (one reason is that the error propagation matrix of inexact coarse-grid correction is not a projection). In this paper, we develop a theoretical framework for the convergence analysis of inexact two-grid methods. More specifically, we present two-sided bounds for the energy norm of the error propagation matrix of inexact two-grid methods, from which one can readily obtain the identity for exact two-grid convergence. As an application, we establish a unified convergence theory for multigrid methods, which allows the coarsest-grid system to be solved approximately.
关键词	multigrid inexact two-grid methods convergence factor eigenvalue analysis
DOI	10.1137/20M1356075
收录类别	SCI
语种	英语
资助项目	National Key R\&D Program of China[2020YFA0711900] ; National Key R\&D Program of China[2020YFA0711904] ; National Science Foundation of China[11971472] ; Key Research Program of Frontier Sciences of CAS
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000765864500006
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60185
专题	计算数学与科学工程计算研究所
通讯作者	Xu, Xuefeng
作者单位	1.Purdue Univ, Dept Math, W Lafayette, IN 47907 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Xu, Xuefeng,Zhang, Chen-Song. CONVERGENCE ANALYSIS OF INEXACT TWO-GRID METHODS: A THEORETICAL FRAMEWORK[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2022,60(1):133-156.
APA	Xu, Xuefeng,&Zhang, Chen-Song.(2022).CONVERGENCE ANALYSIS OF INEXACT TWO-GRID METHODS: A THEORETICAL FRAMEWORK.SIAM JOURNAL ON NUMERICAL ANALYSIS,60(1),133-156.
MLA	Xu, Xuefeng,et al."CONVERGENCE ANALYSIS OF INEXACT TWO-GRID METHODS: A THEORETICAL FRAMEWORK".SIAM JOURNAL ON NUMERICAL ANALYSIS 60.1(2022):133-156.