TY - JOUR
T1 - Monolithic Multigrid for Reduced Magnetohydrodynamic Equations
AU - Zhang , Xiaodi
AU - Zheng , Weiying
JO - Journal of Computational Mathematics
VL - 3
SP - 453
EP - 470
PY - 2021
DA - 2021/04
SN - 39
DO - http://doi.org/10.4208/jcm.2006-m2020-0071
UR - https://global-sci.org/intro/article_detail/jcm/18741.html
KW - Monolithic multigrid, Magnetohydrodynamic equations, Diagonal Braess-Sarazin smoother, Finite element method.
AB - <p style="text-align: justify;">In this paper, the monolithic multigrid method is investigated for reduced magnetohydrodynamic equations. We propose a diagonal Braess-Sarazin smoother for the finite
element discrete system and prove the uniform convergence of the MMG method with
respect to mesh sizes. A multigrid-preconditioned FGMRES method is proposed to solve
the magnetohydrodynamic equations. It turns out to be robust for relatively large physical
parameters. By extensive numerical experiments, we demonstrate the optimality of the
monolithic multigrid method with respect to the number of degrees of freedom.</p>