Speaker: Dr. Daniel R. Reynolds, Southern Methodist University
Abstract:
Continuum-level models for magnetically-confined fusion plasmas result
in large scale, nonlinear, stiff systems of partial differential
equations. Stiffness in these models arises due to a host of sources,
including diffusive processes such as resistivity and viscosity, but
primarily due to the presence of very high speed but low energy
hyperbolic effects. In this talk, I discuss an effort to construct
scalable solvers for a simplified resistive MHD model of fusion plasmas,
based on uniform grid finite volume and fully implicit time
discretizations. At the core of this approach, we solve a large
nonlinear system of equations at each time step, which we accomplish
using classical Newton-Krylov methods. Within this approach, the key
component that enables scalability is an effective preconditioner for
the inner Krylov iterative linear solver. I will discuss our
preconditioning approach, which we have specifically designed to
alleviate stiffness due to fast hyperbolic waves, and I will present
results demonstrating these approaches on a variety of strenuous test
problems.