Monte Carlo Methods for the Neutron Transport Equation

This paper continues our treatment of the neutron transport equation (NTE), building on the work in [A. M. G. Cox et al., J. Stat. Phys., 176 (2019), pp. 425-455; E. Horton, A. E. Kyprianou, and D. Villemonais, Ann Appl. Probab., 30 (2020), pp. 2573-2612; and S. C. Harris, E. Horton, and A. E. Kyprianou, Ann. Appl. Probab., 30 (2020), pp. 2815-2845], which describes the density (equivalently, flux) of neutrons through inhomogeneous fissile media. Our aim is to analyze existing and novel Monte Carlo (MC) algorithms, aimed at simulating the lead eigenvalue associated with the underlying model. This quantity is of principal importance in the nuclear regulatory industry, for which the NTE must be solved on complicated inhomogeneous 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 versus cost, as well as the possibility of more convenient computational parallelization.