A Linear Algebraic Analysis of Diffusion Synthetic Acceleration for the Boltzmann Transport Equation

Abstract

A linear algebraic formulation of discretized, mono-energetic, steady-state, linear Boltzmann transport equations in slab geometry is presented. The discretization consists of a discrete ordinates collocation in angle and a diamond-difference method in space. By expressing Diffusion Synthetic Acceleration in this formalism, asymptotic results are obtained that prove the effectiveness of the associated preconditioner in various asymptotic regimes, including the asymptotic diffusion limit. These results hold for problems with nonconstant coefficients and nonuniform spatial zoning posed on finite domains with an incident flux and/or reflection prescribed at the boundaries. Numerical results are also presented which demonstrate these results.