Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems

A parallel, fully coupled, nonlinearly implicit Newton–Krylov–Schwarz algorithm is proposed for the numerical simulation of a magnetic reconnection problem described by a system of resistive Hall magnetohydrodynamics equations in slab geometry. A key component of the algorithm is a restricted additive Schwarz preconditioner defined for problems with doubly periodic boundary conditions. We show numerically that with such a preconditioned nonlinearly implicit method the time step size is no longer constrained by the CFL number or the convergence of the Newton solver. We report the parallel performance of the algorithm and software on machines with thousands of processors.