Fourier Analysis of Parallel Inexact Block-Jacobi Splitting with Transport Synthetic Acceleration in Slab Geometry

A Fourier analysis is conducted for the discrete-ordinates (SN) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) and Richardson iteration preconditioned with Transport Synthetic Acceleration (TSA), using the Parallel Block-Jacobi (PBJ) algorithm. Both “traditional” TSA (TTSA) and a “modified” TSA (MTSA), in which only the scattering in the low order equations is reduced by some non-negative factor β < 1, are considered. The results for the un-accelerated algorithm show that convergence of the PBJ algorithm can degrade. The PBJ algorithm with TTSA can be effective provided the β parameter is properly tuned for a given scattering ratio c, but is potentially unstable. Compared to TTSA, MTSA is less sensitive to the choice of β, more effective for the same computational effort ( ' c ), and it is unconditionally stable.