Abstract
The Variational Variance Reduction (VVR) method is an effective technique for increasing the efficiency of Monte Carlo simulations [Ann. Nucl. Energy 28 (2001) 457; Nucl. Sci. Eng., in press]. This method uses a variational functional, which employs first-order estimates of forward and adjoint fluxes, to yield a second-order estimate of a desired system characteristic – which, in this paper, is the criticality eigenvalue k. If Monte Carlo estimates of the forward and adjoint fluxes are used, each having global “first-order” errors of O(1/ N ) , where N is the number of histories used in the Monte Carlo simulation, then the statistical error in the VVR estimation of k will in principle be O(1/ N). In this paper, we develop this theoretical possibility and demonstrate with numerical examples that implementations of the VVR method for criticality problems can approximate O(1/ N) convergence for significantly large values of N.
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