Monte-Carlo Methods for the Neutron Transport Equation

Alexander M. G. Cox, Simon C. Harris, Andreas E. Kyprianou, Minmin Wang

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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 in homogenous 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 parallelization.
Original languageEnglish
Pages (from-to)775-825
Number of pages51
JournalSIAM/ASA Journal on Uncertainty Quantification
Issue number2
Early online date30 Jun 2022
Publication statusPublished - 31 Dec 2022

Bibliographical note

Funding Information:
∗Received by the editors January 7, 2021; accepted for publication (in revised form) January 4, 2022; published electronically June 30, 2022. Funding: This work was supported by EPSRC grant EP/P009220/1. †Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK ( ‡Department of Statistics, University of Auckland, Auckland 1142, New Zealand ( §School of Mathematical and Physical Sciences, University of Sussex, Brighton, BN1 9RH, UK (wangminmin03@

Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics Publications. All rights reserved.


  • Doob h-transform
  • Monte Carlo simulation
  • Perron–Frobenius decomposition
  • complexity
  • neutron transport equation
  • principal eigenvalue
  • semigroup theory
  • twisted Monte Carlo

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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