Effect of Material Heterogeneity on the Performance of DSA for Even-Parity S_n Methods

A spectral analysis is conducted for the Source Iteration (SI), and Diffusion Synthetic Acceleration (DSA) operators previously formulated for solving the Even-Parity Method (EPM) equations. In order to accommodate material heterogeneity, the analysis is performed for the Periodic Horizontal Interface (PHI) configuration. The dependence of the spectral radius on the optical thickness of the two PHI layers illustrates the deterioration in the rate of convergence with increasing material discontinuity, especially when one of the layers approaches a void. The rate at which this deterioration occurs is determined for a specific material discontinuity in order to demonstrate the conditional robustness of the EPM-DSA iterations. The results of the analysis are put in perspective via numerical tests with the DANTE code (MCGhee, et al., 1997) which exhibits a deterioration in the spectral radius consitent with the theory