A robust solver for the finite element approximation of stationary incompressible MHD equations in 3D
This work provides an efficient solver for 3D MHD simulations, which is important for computational fluid dynamics and plasma physics, though the improvements are incremental.
The authors propose a robust preconditioner for the GMRES solver applied to finite element discretizations of stationary incompressible MHD equations in 3D, demonstrating optimal scalability with respect to degrees of freedom and robustness for moderate physical parameters through three numerical experiments.
In this paper, we propose a robust solver for the finite element discrete problem of the stationary incompressible magnetohydrodynamic (MHD) equations in three dimensions. By the mixed finite element method, both the velocity and the pressure are approximated by H1-conforming finite elements, while the magnetic field is approximated by H(curl)-conforming edge elements. An efficient preconditioner is proposed to accelerate the convergence of the GMRES method for solving the linearized MHD problem. We use three numerical experiments to demonstrate the effectiveness of the finite element method and the robustness of the discrete solver. The preconditioner contains the least undetermined parameters and is optimal with respect to the number of degrees of freedom. We also show the scalability of the solver for moderate physical parameters.