Monolithic Multigrid for Reduced Magnetohydrodynamic Equations (Journal of Computational Mathematics, 2021)
In this paper, the monolithic multigrid method is investigated for reduced magnetohydrodynamic equations. We propose a diagonal Braess-Sarazin smoother for the finiteelement discrete system and prove the uniform convergence of the MMG method withrespect to mesh sizes. A multigrid-preconditioned FGMRES method is proposed to solvethe magnetohydrodynamic equations. It turns out to be robust for relatively large physicalparameters. By extensive numerical experiments, we demonstrate the optimality of themonolithic multigrid method with respect to the number of degrees of freedom.