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 -

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.