TY - JOUR
T1 - A charge-conservative finite element method for inductionless MHD equations. Part II
T2 - A robust solver
AU - Li, Lingxiao
AU - Ni, Mingjiu
AU - Zheng, Weiying
N1 - Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Augmented Lagrangian finite element method
KW - Block preconditioner
KW - Conservation of charges
KW - Field-of-values-equivalence
KW - Inductionless MHD equations
UR - https://www.scopus.com/pages/publications/85071944567
U2 - 10.1137/19M1260372
DO - 10.1137/19M1260372
M3 - 文章
AN - SCOPUS:85071944567
SN - 1064-8275
VL - 41
SP - B816-B842
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 4
ER -