Comparison of hybrid methods for global variance reduction in shielding calculations

For Monte Carlo shielding problems that calculate a mesh tally over the entire problem, the statistical uncertainties computed for each voxel can vary widely. This can lead to unacceptably long run times in order to reduce the uncertainties in all areas of the problem to a reasonably low level. Hybrid methods - using estimates from deterministic calculations to create importance maps for variance reduction in Monte Carlo calculations - have been successfully used to optimize the calculation of specific tallies. For the global problem, several methods have been proposed to create importance maps that distribute Monte Carlo particles in such a way as to achieve a more uniform distribution of relative uncertainty across the problem. The goal is to compute a mesh tally with nearly the same relative uncertainties in the low flux/dose areas as in the high flux/dose areas. Methods based on only forward deterministic estimates and methods using both forward and adjoint deterministic methods have been implemented in the SCALE/MAVRIC package and have been compared against each other by computing global mesh tallies on several representative shielding problems. Methods using both forward and adjoint estimates provide better performance for computing more uniform relative uncertainties across a global mesh tally.