Singular value decomposition of adjoint flux distributions for Monte Carlo variance reduction

Abstract

Monte Carlo (MC) shielding calculations often use weight windows (WWs) and biased sources formed from a deterministic estimate of the adjoint flux to improve the convergence rate of tallies. This requires a significant amount of computer memory, which can limit the memory available for high-resolution tally output. A new method is proposed for reducing these memory requirements by using singular value decomposition (SVD) in linear or logarithmic space to approximate the adjoint flux. This method’s performance is evaluated using the Shift and Denovo codes for streaming and diffusion base case problems, followed by problems using the Westinghouse AP1000 and the Joint European Torus. The log SVD reduced WW memory requirements by an order of magnitude in all cases without a significant performance penalty. Additionally, the linear SVD reduced biased source memory requirements by an order of magnitude, but further investigation is needed to account for observed limitations.