Nonlinear extended magnetohydrodynamics simulation using high-order finite elements

Peak performance for magnetically confined fusion plasmas occurs near thresholds of instability for macroscopic modes that distort and possibly disrupt equilibrium conditions. In some cases, however, the best approach is to exceed stability thresholds and rely upon nonlinear saturation effects. Understanding this behaviour is essential for achieving ignition in future burning plasma experiments, and advances in large-scale numerical simulation have an important role. High-order finite elements permit accurate representation of extreme anisotropies associated with the magnetic field, and a new implicit algorithm has been developed for advancing the two-fluid model. Implementation of parallel direct methods for solving the sparse matrices makes the approach practical. The resulting performance improvements are presently being applied to investigate the evolution of 'edge localized modes' including important drift effects.