A modified Monte Carlo “Local Importance Function Transform” method

The Local Importance Function Transform (LIFT) method uses an approximation of the contributon transport problem to bias a forward Monte-Carlo (MC) source-detector simulation (Turner, 1996, Turner and Larsen, 1997a, Turner and Larsen, 1997b). Local (cell-based) biasing parameters are calculated from an inexpensive deterministic adjoint solution and used to modify the physics of the forward transport simulation. In this paper, we develop a new expression for the LIFT biasing parameter, which depends on a cell-average adjoint current-to-scalar flux (J*/ϕ*) ratio. This biasing parameter differs significantly from the original expression, which uses adjoint cell-edge scalar fluxes to construct a finite difference estimate of the flux derivative; the resulting (original LIFT) biasing parameters exhibit spikes in magnitude at material discontinuities, causing the method to lose efficiency in problems with high spatial heterogeneity. The new J*/ϕ* expression, while more expensive to obtain, generates biasing parameters that vary smoothly across the spatial domain. The result is an improvement in simulation efficiency. A representative test problem has been developed and analyzed to demonstrate the advantage of the updated biasing parameter expression with regards to solution figure of merit (FOM). For reference, the two variants of the LIFT method are compared to a similar variance reduction method developed by Depinay (1997) and Depinay et al. (2006), as well as MC with deterministic adjoint weight windows (WW).