Comparison of variance reduction methods in shielding problems with source multiplication

The solution of the Boltzmann equation for particle transport is the central problem of radiation shielding. When the solution is attempted using Monte Carlo methods, the use of variance reduction techniques is unavoidable, because the probability that a source particle reaches the detector is, by construction, very small. This paper presents a comparative study of a few state-of-the-art variance reduction techniques in the context of problems with source multiplication, e.g. in the presence of fissile material. This slightly unusual setting is found to be intractable for some variance reduction techniques. Based on our simulation results, we formulate specific recommendations for the treatment of this class of problems.