Accelerated JFNK via compressed sensing of near-sparse Jacobians

The Jacobian-free Newton-Krylov (JFNK) method is a powerful method for root-finding of black-box nonlinear continuous multidimensional real-valued functions. Recently developed enhancements to the conventional JFNK algorithm are presented, with emphasis on cases where the function evaluations are the dominant cost. In particular, the use of a novel approach to compressed sensing to reconstruct a sparse (or near-sparse) Jacobian matrix using only information from the available subspace, for use as a dynamic preconditioner, has been demonstrated to provide a significant speed-up in relevant cases. Results of the new JFNK code applied to TFTR MHD equilibria using the Princeton Iterative Equilibrium Solver (PIES) are also presented.