Author: Tom Manteuffel, Applied Mathematics Department, University of Colorado at Boulder
Title: Nested Iteration First-Order Least Squares on Incompressible Resistive Magnetohydrodynamics
Magnetohydrodynamics (MHD) is a fluid theory that describes Plasma Physics by treating the plasma as a fluid of charged particles. Hence, the equations that describe the plasma form a nonlinear system that couples Navier-Stokes with Maxwell's equations. We describe how the FOSLS method can be applied to incompressible resistive MHD to yield an well posed, H^1 equivalent functional minimization. To solve this system, a nested-iteration-Newton-FOSLS-AMG approach is taken. Much of the work is done on relatively coarse grids, including most of the linearizations. We show that at most one Newton step and a few V-cycles are all that is needed on the finest grid. Estimates of the local error and of relevant problem parameters that are established while ascending through the sequence of nested grids are used to direct adaptive local mesh refinement. An algebraic multigrid solver is used to solve the linearization steps.
Numerical results are presented for two instabilities in a large aspect-ratio tokamak, the tearing mode and the island coalesence mode. The goal is to resolve as much physics with the least amount of computational work. We show that this is achieved in a few dozen work units (A work unit equals a fine grid residual evaluation).
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