Scalable parallel implicit solvers for 3D magnetohydrodynamics

The efficient integration of the extended magnetohydrodynamics (XMHD) model is critical for present and future modeling needs of fusion plasmas and is at the core of several interacting SciDAC centers. However, XMHD is a remarkably challenging system of PDEs, featuring a stiff multiscale character both in time and space. Such stiff character has hindered progress toward a truly scalable, efficient, and accurate nonlinear XMHD algorithm. In this paper, we discuss recent algorithmic developments that demonstrate that such an XMHD algorithm is within reach. The approach is based on fully implicit time integration and employs parallel Jacobian-free Newton-Krylov technology, preconditioned with multigrid methods for algorithmic scalability. The algorithm has been tested on a variety of 2D and 3D configurations that demonstrate its excellent algorithmic scalability properties, both serially and in parallel up to 4096 processors and 134 million unknowns.