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Uzawa methods for a class of block three-by-three saddle-point problems
Huang, Na1; Dai, Yu-Hong2,3; Hu, QiYa2,3
AbstractIn 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.
Keywordinexact Uzawa method saddle-point problem Uzawa method
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000485829600001
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Document Type期刊论文
Corresponding AuthorDai, Yu-Hong
Affiliation1.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
Recommended Citation
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.
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