Speaker: Dr. Daniel R. Reynolds, Southern Methodist University
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.