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

文献类型：期刊论文

作者Huang, Na2; Dai, Yu-Hong1,3; Hu, QiYa1,3
刊名NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
出版日期2019-09-05
页码26
关键词inexact Uzawa method saddle-point problem Uzawa method
ISSN号1070-5325
DOI10.1002/nla.2265
英文摘要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.
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
语种英语
WOS记录号WOS:000485829600001
出版者WILEY
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/35563]  
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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
2.China Agr Univ, Coll Sci, Dept Appl Math, Beijing, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, 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.

入库方式： OAI收割

来源：数学与系统科学研究院

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