A Diffusion-Synthetic Acceleration Technique for the Even-Parity<i>S_n</i>Equations with Anisotropic Scattering

Abstract

A source iteration scheme and associated diffusion-synthetic acceleration scheme are defined for the even-parity Sn equations with anisotropic scattering. The spatially analytic versions of these schemes are shown to be completely equivalent to their counterparts for the first-order form of the equations. Thus, in the limit as the spatial mesh is refined, each even-parity iteration scheme must asymptotically converge at the same rate as its first-order counterpart. The equivalence of the even-parity and first-order source iteration processes implies that any synthetic acceleration scheme for the first-order Sn equations has an even-parity counterpart that is equivalent for the spatially analytic case. Theoretical and computational results are given that demonstrate the properties of the even-parity source iteration and diffusion-synthetic acceleration schemes.