A CHARGE-CONSERVATIVE FINITE ELEMENT METHOD FOR INDUCTIONLESS MHD EQUATIONS. PART II: A ROBUST SOLVER

被引：14
|
作者：
Li, Lingxiao [1 ]
Ni, Mingjiu [2 ]
Zheng, Weiying [3 ]
机构：
[1] 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
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2019年 / 41卷 / 04期
关键词：
inductionless MHD equations; block preconditioner; field-of-values-equivalence; conservation of charges; augmented Lagrangian finite element method; MAGNETIC REYNOLDS-NUMBER; NAVIER-STOKES EQUATIONS; BLOCK PRECONDITIONERS; OSEEN PROBLEM; STABILIZATION; FORMULATION; SCHEME; FLOWS;
D O I：
10.1137/19M1260372
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In [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.
引用
收藏
页码：B816 / B842
页数：27
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