A LINEAR ALGEBRAIC ANALYSIS OF DIFFUSION SYNTHETIC ACCELERATION FOR THE BOLTZMANN TRANSPORT-EQUATION

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