Adjoint-based path length stretching in a Woodcock framework with SIRS angular biasing

Abstract

The development of an adjoint-based path-stretching scheme within a non-analog Woodcock (delta-tracking) framework is predicated on zero-variance formalism. The derivation of an ideal cross-section stretching factor is possible from the incident and the outgoing adjoint collision densities. The incorporation of this bias into the virtual collision decision probability necessitates time-consuming oversampling (high sampling cross section) to achieve low variance. Conversely, a similar effect can be achieved by stretching the sampling cross section, which, however, results in a considerable increase in variance, even for minor discrepancies between the actual local and the sampling cross sections. To mitigate this, a combination of the two bias methods is necessary. Nevertheless, sensitivity to the difference between sampling and actual cross sections persists, which limits the maximum efficiency gain. To address this challenge, a Sampling Importance Resampling (SIRS) scheme was devised for angular biasing, as both transport and collision kernels necessitate biasing for a significant enhancement in efficiency. The efficacy of the algorithm is demonstrated through numerical examples for source-detector systems, employing realistic geometries and utilizing the GUARDYAN code.