Uzawa methods for a class of block three-by-three saddle-point problems

doi:10.1002/nla.2265

	Uzawa methods for a class of block three-by-three saddle-point problems
	Huang, Na 1; Dai, Yu-Hong2,3 ; Hu, QiYa2,3
	2019-09-05
发表期刊	NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
ISSN	1070-5325
页码	26
摘要	In this work, we consider numerical methods for solving a class of block three-by-three saddle-point problems, which arise from finite element methods for solving time-dependent Maxwell equations and some other applications. The direct extension of the Uzawa method for solving this block three-by-three saddle-point problem requires the exact solution of a symmetric indefinite system of linear equations at each step. To avoid heavy computations at each step, we propose an inexact Uzawa method, which solves the symmetric indefinite linear system in some inexact way. Under suitable assumptions, we show that the inexact Uzawa method converges to the unique solution of the saddle-point problem within the approximation level. Two special algorithms are customized for the inexact Uzawa method combining the splitting iteration method and a preconditioning technique, respectively. Numerical experiments are presented, which demonstrated the usefulness of the inexact Uzawa method and the two customized algorithms.
关键词	inexact Uzawa method saddle-point problem Uzawa method
DOI	10.1002/nla.2265
语种	英语
资助项目	National Postdoctoral Program for Innovative Talents[BX201600182] ; China Postdoctoral Science Foundation[2016M600141] ; Chinese NSF[11631013] ; Chinese NSF[11331012] ; Chinese NSF[71331001] ; Chinese NSF[11971372] ; Key Project of Chinese National Programs for Fundamental Research and Development[2015CB856002] ; National Natural Science Foundation of China[G11571352]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000485829600001
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35564
专题	计算数学与科学工程计算研究所
通讯作者	Dai, Yu-Hong
作者单位	1.China Agr Univ, Coll Sci, Dept Appl Math, Beijing, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Huang, Na,Dai, Yu-Hong,Hu, QiYa. Uzawa methods for a class of block three-by-three saddle-point problems[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2019:26.
APA	Huang, Na,Dai, Yu-Hong,&Hu, QiYa.(2019).Uzawa methods for a class of block three-by-three saddle-point problems.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,26.
MLA	Huang, Na,et al."Uzawa methods for a class of block three-by-three saddle-point problems".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS (2019):26.