Monte Carlo methods for the neutron transport equation

This paper continues our treatment of the Neutron Transport Equation (NTE) building on the work in [13], [28] and [25], which describes the density (equiv. flux) of neutrons through inhomogeneous fissile medium. Our aim is to analyse existing and novel Monte Carlo (MC) algorithms, aimed at simu- lating the lead eigenvalue associated with the underlying model. This quantity is of principal importance in the nuclear regula- tory industry for which the NTE must be solved on complicated inhomogenous domains corresponding to nuclear reactor cores, irradiative hospital equipment, food irradiation equipment and so on. We include a complexity analysis of such MC algorithms, noting that no such undertaking has previously appeared in the literature. The new MC algorithms offer a variety of advantages and disadvantages of accuracy vs cost, as well as the possibility of more convenient computational parallelisation.