A robust solver for the finite element approximation of stationary incompressible MHD equations in 3D

doi:10.1016/j.jcp.2017.09.025

	A robust solver for the finite element approximation of stationary incompressible MHD equations in 3D
	Li, Lingxiao 1,2; Zheng, Weiying1,2
	2017-12-15
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	351 页码:254-270
摘要	In 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.
关键词	Incompressible magnetohydrodynamic equations Mixed finite element method Block preconditioner grad-div stabilization Newton's method
DOI	10.1016/j.jcp.2017.09.025
语种	英语
资助项目	China NSF[91430215] ; National Magnetic Confinement Fusion Science Program[2015GB110003]
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000415304900014
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26833
专题	计算数学与科学工程计算研究所
通讯作者	Zheng, Weiying
作者单位	1.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
推荐引用方式 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.