Hybrid Monte Carlo estimators for multilayer transport problems

This paper introduces a new family of hybrid estimators aimed at controlling the efficiency of Monte Carlo computations in particle transport problems. In this context, efficiency is usually measured by the figure of merit (FOM) given by the inverse product of the estimator variance Var[ξ] and the run time T: FOM := (Var[ξ] T)^-1. Previously, we developed a new family of transport-constrained unbiased radiance estimators (T-CURE) that generalize the conventional collision and track length estimators [1] and provide 1-2 orders of magnitude additional variance reduction. However, these gains in variance reduction are partly offset by increases in overhead time [2], lowering their computational efficiency. Here we show that combining T-CURE estimation with conventional terminal estimation each individual biography can moderate the efficiency of the resulting "hybrid" estimator without introducing bias in the computation. This is achieved by treating only the refractive interface crossings with the extended next event estimator, and all others by standard terminal estimators. This is because when there are index-mismatched interfaces between the collision location and the detector, the T-CURE computation rapidly becomes intractable due to the large number of refractions and reflections that can arise. We illustrate the gains in efficiency by comparing our hybrid strategy with more conventional estimation methods in a series of multi-layer numerical examples.