Variance estimation in domain decomposed Monte Carlo eigenvalue calculations

The number of tallies performed in a given Monte Carlo calculation is limited in most modern Monte Carlo codes by the amount of memory that can be allocated on a single processor. By using domain decomposition, significantly more tallies can be performed because the calculation is now limited by the total amount of memory available on all processors. Unfortunately, decomposing the problem geometry also introduces significant issues with the way tally statistics are conventionally calculated. In order to deal with the issue of calculating tally variances in domain decomposed environments for the Shift hybrid Monte Carlo code, this paper presents an alternative approach for reactor scenarios in which an assumption is made that once a particle leaves a domain, it does not reenter the domain. Particles that reenter the domain are instead treated as separate independent histories. This assumption introduces a bias that generally leads to under-prediction of the calculated variances for tallies within a few mean free paths of the domain boundaries. However, through the use of different decomposition strategies, primarily overlapping domains, the under-prediction in the calculated uncertainties is significantly reduced. In the cases considered in these analyses, and using domains with an overlap fraction of 0.5, the estimated error in the standard deviation for all tally cells is within 20%, within 10% for over 99% of the tally cells, and within 5% for over 75% of the tally cells.