Monte-Carlo Methods for the Neutron Transport Equation

TL;DR

This paper analyzes Monte Carlo algorithms for solving the Neutron Transport Equation, focusing on estimating the principal eigenvalue crucial for nuclear industry applications, and provides a novel complexity analysis of these methods.

Contribution

It introduces and analyzes new Monte Carlo algorithms for the Neutron Transport Equation, including a detailed complexity analysis not previously available.

Findings

New Monte Carlo algorithms with different accuracy and cost trade-offs

Complexity analysis of Monte Carlo methods for NTE

Potential for improved parallelization of simulations

Abstract

This paper continues our treatment of the Neutron Transport Equation (NTE) building on the work in [arXiv:1809.00827v2], [arXiv:1810.01779v4] and [arXiv:1901.00220v3], which describes the flux of neutrons through inhomogeneous fissile medium. Our aim is to analyse 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 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.