Island Coalescence Using Parallel First-Order System Least Squares on Incompressible Resistive Magnetohydrodynamics

Abstract

This paper investigates the performance of a parallel Newton, first-order system least-squares (FOSLS) finite-element method with local adaptive refinement and algebraic multigrid (AMG) applied to incompressible, resistive magnetohydrodynamics. In particular, an island coalescence test problem is studied that models magnetic reconnection using a reduced two-dimensional (2D) model of a tokamak fusion reactor. The results show that, using an appropriate temporal and spatial resolution, these methods are capable of resolving the physical instabilities accurately at small computational cost. The time-dependent, nonlinear system of PDEs is solved using work equivalent to about 50--60 simple relaxation sweeps (Gauss--Seidel iterations) per time step. Experiments show that, unless the time step is sufficiently small, nonphysical numerical instabilities may occur. Further, decreasing the time step size does not proportionally increase the cost of the computation, because AMG convergence is improved. In addition, an effective implementation of the methods in parallel keeps load balancing issues to a minimum. Various quantities, such as the reconnection rate and the “sloshing” effect of the plasma instability, are measured to confirm that the correct physics is reproduced.