Application of Nonlinear Krylov Acceleration to Radiative Transfer Problems

Andrew Till, Texas A&M University

The iterative solution technique used for nonlinear partial differential equation systems normally is nested, with outer, nonlinear iterations and inner, linearized iterations. We implement a nonlinear Krylov acceleration (NKA) method in the PDT code and apply it to the radiative transfer system. NKA breaks the nesting, resulting in more outer (thermal) iterations, but significantly fewer total inner (transport) iterations. Using the metric of total inner transport iterations, we investigate a crooked-pipe-like problem and a pseudo-shock-tube problem. Using only sweep preconditioning, we compare NKA against a typical inner/outer method employing GMRES/Newton and find NKA to be comparable or superior. Finally, we demonstrate the efficacy of applying diffusion-based preconditioning to grey problems in conjunction with NKA.

Abstract Author(s): Andrew T. Till, Marvin L. Adams, Jim E. Morel