A Preconditioned Newton-Krylov Code for Calculating 3D MHD Equilibria with Magnetic Islands

We have implemented a Jacobian-free Newton-Krylov method with a Levenberg-Marquardt line-search in the PIES code, which solves for 3D MHD equilibria. The algorithm has performed well in tests on helical equilibria with islands. We are investigating further techniques, such as using an adaptive preconditioner, where the limited subspace information from each linear solve is used to construct a preconditioner for future linear solves.