Stability Analysis of Synthetic Acceleration Methods with Anisotropic Scattering

A study of the spectral radius for the continuous form of the source iteration, diffusion synthetic acceleration, and various P_L acceleration methods (L ≥ 1) for anisotropically scattering neutron transport is carried out via a Fourier stability analysis. The purpose of the study is to determine which acceleration scheme is optimum. The problem is formulated as a matrix eigenvalue problem with, in general, N + 1 iteration eigenvalues ω where N denotes the degree of anisotropy. The P₁ acceleration method is determined as the most efficient P_L approach for the cases of linearly and quadratically anisotropic scattering.