S2SA preconditioning for the Sn equations with strictly nonnegative spatial discretization

Abstract

Preconditioners based upon transport sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D Sn transport equation using a strictly nonnegative nonlinear spatial closure. Linear and nonlinear preconditioners have been derived and analyzed. The effectiveness of various combinations of these preconditioners are compared using the source iteration, matrix-free Picard Krylov, and nonlinear Krylov acceleration methods. In one dimension, preconditioning with a linear S2SA diffusion equation is found to be essentially equivalent to using a nonlinear diffusion equation. The ability to use a linear diffusion equation has important implications for preconditioning the Sn equations with a strictly nonnegative spatial discretization in multiple dimensions.