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Adjoint methods form a class of importance sampling methods that are used toaccelerate Monte Carlo (MC) simulations of transport equations. Ideally,adjoint methods allow for zero-variance MC estimators provided that thesolution to an adjoint transport equation is known. Hybrid methods aim at (i)approximately solving the adjoint transport equation with a deterministicmethod; and (ii) use the solution to construct an unbiased MC samplingalgorithm with low variance. The problem with this approach is that both stepscan be prohibitively expensive. In this paper, we simplify steps (i) and (ii)by calculating only parts of the adjoint solution. More specifically, in ageometry with limited volume scattering and complicated reflection at theboundary, we consider the situation where the adjoint solution "neglects"volume scattering, whereby significantly reducing the degrees of freedom insteps (i) and (ii). A main application for such a geometry is in remote sensingof the environment using physics-based signal models. Volume scattering is thenincorporated using an analog sampling algorithm (or more precisely a simplemodification of analog sampling called a heuristic sampling algorithm) in orderto obtain unbiased estimators. In geometries with weak volume scattering (witha domain of interest of size comparable to the transport mean free path), wedemonstrate numerically significant variance reductions and speed-ups (figuresof merit).

Importance Sampling and Adjoint Hybrid Methods in Monte Carlo Transport with Reflecting Boundaries