Preconditioning for Three-Dimensional Two-Fluid NIMROD Applications

A new parallel preconditioner implementation for Krylov-space matrix-solves in nonlinear 3D two-fluid simulations with the NIMROD code (nimrodteam.org) is presented. The implementation takes advantage of the typically small perturbation size. The large axisymmetric component provides diagonal dominance for matrices partitioned into Fourier-component blocks. An inner preconditioner iteration using limited Fourier-component coupling in Gauss-Seidel-like relaxation with diagonal blocks solved by SuperLU-DIST [Li and Demmel, ACM Trans. Math. Software 29, 110 (2003)] is then effective for the two-fluid magnetic advance, provided that a realistic level of electron inertia is used to limit R-mode frequencies. Generating and multiplying matrix elements for a limited number of off-diagonal blocks is shown to scale with processor number as the number of Fourier components is increased in research-relevant sawtooth and ELM computations.