Comparison of P(sub 1) and simplified P(sub 2) synthetic acceleration for iterative methods in transport solutions

摘要

Using an operator form of a synthetic acceleration method, we derive the P(sub 1)- and a new second-moment P(sub 2)-acceleration schemes. We analyze the convergence rate of each scheme by Performing a Fourier analysis. The second-moment P(sub 2)-acceleration outperforms an earlier third-moment P(sub 2)-acceleration method by Miller and Larsen. However, it is still less efficient than P(sub l)-acceleration (diffusion synthetic acceleration: DSA). These results confirm that one cannot simply assume that replacement of the DSA method with a higher order operator will lead to a smaller spectral radius. We get similar results for the P(sub l)- and simplified P(sub 2)-acceleration in two-dimensional x-y geometry.