A variationally-based variance reduction method for Monte Carlo neutron transport calculations

A new variationally-based Monte Carlo variance reduction (VVR) method is developed to improve the estimation of characteristic parameters for neutron shielding and criticality pro- blems. The VVR method employs a variationally-motivated functional that processes ``low- qualityʹʹ global forward and adjoint ¯ux estimates into ``high-qualityʹʹ characteristic para- meter estimates, such as the transmitted current through a shield or an eigenvalue. The VVR functionals are more costly to evaluate than standard functionals used to obtain Monte Carlo estimates, but they are more accurate. In this paper we demonstrate that for mono-energetic 1-D shielding and eigenvalue test problems, the improvement in accuracy obtained from the VVR scheme outweighs the extra computational expense, yielding a signi®cant gain in the ®gure of merit