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A robust solver for the finite element approximation of stationary incompressible MHD equations in 3D
Li, Lingxiao1,2; Zheng, Weiying1,2
2017-12-15
Source PublicationJOURNAL OF COMPUTATIONAL PHYSICS
ISSN0021-9991
Volume351Pages:254-270
AbstractIn this paper, we propose a Newton-Krylov solver and a Picard-Krylov solver for finite element discrete problem of stationary incompressible magnetohydrodynamic equations in three dimensions. Using a mixed finite element method, we discretize the velocity and the pressure by H-1(Omega)-conforming finite elements and discretize the magnetic field by H(curl, Omega)-conforming edge elements. An efficient preconditioner is proposed to accelerate the convergence of GMRES method for solving linearized discrete problems. By extensive numerical experiments, we demonstrate the robustness of the Newton-Krylov solver for relatively large physical parameters and the optimality with respect to the number of degrees of freedom. Moreover, the numerical experiments show that the Newton-Krylov solver is more robust than the Picard-Krylov solver for large Reynolds number. (C) 2017 Elsevier Inc. All rights reserved.
KeywordIncompressible magnetohydrodynamic equations Mixed finite element method Block preconditioner grad-div stabilization Newton's method
DOI10.1016/j.jcp.2017.09.025
Language英语
Funding ProjectChina NSF[91430215] ; National Magnetic Confinement Fusion Science Program[2015GB110003]
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000415304900014
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26833
Collection计算数学与科学工程计算研究所
Corresponding AuthorZheng, Weiying
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS,LSEC, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Li, Lingxiao,Zheng, Weiying. A robust solver for the finite element approximation of stationary incompressible MHD equations in 3D[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2017,351:254-270.
APA Li, Lingxiao,&Zheng, Weiying.(2017).A robust solver for the finite element approximation of stationary incompressible MHD equations in 3D.JOURNAL OF COMPUTATIONAL PHYSICS,351,254-270.
MLA Li, Lingxiao,et al."A robust solver for the finite element approximation of stationary incompressible MHD equations in 3D".JOURNAL OF COMPUTATIONAL PHYSICS 351(2017):254-270.
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