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A CHARGE-CONSERVATIVE FINITE ELEMENT METHOD FOR INDUCTIONLESS MHD EQUATIONS. PART II: A ROBUST SOLVER
Li, Lingxiao1; Ni, Mingjiu2; Zheng, Weiying3
2019
Source PublicationSIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN1064-8275
Volume41Issue:4Pages:B816-B842
AbstractIn [L. Li, M. Ni, and W. Zheng, SIAM J. Sci. Comput., 41 (2019), pp. B796-B815] a charge-conservative finite element method is proposed for solving inductionless and incompressible magnetohydrodynamic (MHD) equations. The purpose of this paper is to propose a robust solver for the discrete problem. Using the framework of field-of-values-equivalence, we first study the preconditioned Krylov space method for the continuous problem in the setting of Hilbert spaces. The algebraic preconditioner for the discrete problem is then obtained by representing the preconditioner for the continuous problem in finite element spaces. By three numerical examples, the optimality of the solver to the number of unknowns is demonstrated for both stationary and time-dependent MHD problems.
Keywordinductionless MHD equations block preconditioner field-of-values-equivalence conservation of charges augmented Lagrangian finite element method
DOI10.1137/19M1260372
Language英语
Funding ProjectChina NSF[51636009] ; China NSF[91430215] ; National Science Fund for Distinguished Young Scholars[11725106] ; National Magnetic Confinement Fusion Science Program[2015GB110003]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000483924100034
PublisherSIAM PUBLICATIONS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/33323
Collection计算数学与科学工程计算研究所
Corresponding AuthorLi, Lingxiao
Affiliation1.Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China
2.Univ Chinese Acad Sci, Sch Engn Sci, Beijing 101407, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp Acad Math & Sy, NCMIS,LSEC, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Li, Lingxiao,Ni, Mingjiu,Zheng, Weiying. A CHARGE-CONSERVATIVE FINITE ELEMENT METHOD FOR INDUCTIONLESS MHD EQUATIONS. PART II: A ROBUST SOLVER[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2019,41(4):B816-B842.
APA Li, Lingxiao,Ni, Mingjiu,&Zheng, Weiying.(2019).A CHARGE-CONSERVATIVE FINITE ELEMENT METHOD FOR INDUCTIONLESS MHD EQUATIONS. PART II: A ROBUST SOLVER.SIAM JOURNAL ON SCIENTIFIC COMPUTING,41(4),B816-B842.
MLA Li, Lingxiao,et al."A CHARGE-CONSERVATIVE FINITE ELEMENT METHOD FOR INDUCTIONLESS MHD EQUATIONS. PART II: A ROBUST SOLVER".SIAM JOURNAL ON SCIENTIFIC COMPUTING 41.4(2019):B816-B842.
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