ANGULAR MULTIGRID ACCELERATION FOR PARALLEL SN METHOD WITH APPLICATION TO SHIELDING PROBLEMS

摘要

New acceleration formulations, which are compatible with the adaptive differencing strategy andrnparallel environments, are required. For this purpose, we have developed the Simplified AngularrnMultigrid (SAM), Nested Iteration (NI), and V-Cycle algorithms, and their variousrncombinations, and implemented them in the PENTRANTM 3-D Parallel SN code. Thesernformulations have been examined for a test problem using a variety of parameters includingrndifferent scattering ratios, coarse- and fine-grid convergence tolerances and quadrature orders.rnThe effectiveness of the new multigrid formulations is compared to the standard Partial CurrentrnRebalance (PCR) acceleration method. Thus far, the combinations of SAM and PCR or NI andrnPCR have proved to be very effective for a large range of c-ratios. We have achieved speedupsrnas high as a factor of ~7.3 in the number of iterations, or a factor of ~4.0 in the CPU time.rnPreliminary studies indicate that other combinations such as SAM+V-cycle+PCR or NI+Vcycle+rnPCR can be even more effective in certain problem conditions.