A Conservative Finite Element Solver for MHD Kinematics equations: Vector Potential method and Constraint Preconditioning
Abstract
A new conservative finite element solver for the three-dimensional steady magnetohydrodynamic (MHD) kinematics equations is presented.The solver utilizes magnetic vector potential and current density as solution variables, which are discretized by H(curl)-conforming edge-element and H(div)-conforming face element respectively. As a result, the divergence-free constraints of discrete current density and magnetic induction are both satisfied. Moreover the solutions also preserve the total magnetic helicity. The generated linear algebraic equation is a typical dual saddle-point problem that is ill-conditioned and indefinite. To efficiently solve it, we develop a block preconditioner based on constraint preconditioning framework and devise a preconditioned FGMRES solver. Numerical experiments verify the conservative properties, the convergence rate of the discrete solutions and the robustness of the preconditioner.
Cite
@article{arxiv.2111.11693,
title = {A Conservative Finite Element Solver for MHD Kinematics equations: Vector Potential method and Constraint Preconditioning},
author = {Xujing Li and Lingxiao Li},
journal= {arXiv preprint arXiv:2111.11693},
year = {2022}
}
Comments
13 pages. arXiv admin note: text overlap with arXiv:1712.08922