Monte-Carlo Methods for the Neutron Transport Equation

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

doi:10.1137/21M1390578

Monte-Carlo Methods for the Neutron Transport Equation

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

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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 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 language	English
Pages (from-to)	775-825
Number of pages	51
Journal	SIAM/ASA Journal on Uncertainty Quantification
Volume	10
Issue number	2
Early online date	30 Jun 2022
DOIs	https://doi.org/10.1137/21M1390578
Publication status	Published - 31 Dec 2022

Keywords

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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10.1137/21M1390578

MCNTE_Final_Submitted
© 2022 Society for Industrial and Applied Mathematics
Accepted author manuscript, 1.57 MB
2012.02864v1

Cite this

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title = "Monte-Carlo Methods for the Neutron Transport Equation",

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 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.",

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author = "Cox, {Alexander M. G.} and Harris, {Simon C.} and Kyprianou, {Andreas E.} and Minmin Wang",

note = "Funding Information: ∗Received by the editors January 7, 2021; accepted for publication (in revised form) January 4, 2022; published electronically June 30, 2022. https://doi.org/10.1137/21M1390578 Funding: This work was supported by EPSRC grant EP/P009220/1. †Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK (a.m.g.cox@bath.ac.uk a.kyprianou@bath.ac.uk). ‡Department of Statistics, University of Auckland, Auckland 1142, New Zealand (simon.harris@auckland.ac.nz). §School of Mathematical and Physical Sciences, University of Sussex, Brighton, BN1 9RH, UK (wangminmin03@ gmail.com). Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics Publications. All rights reserved.",

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AU - Cox, Alexander M. G.

AU - Harris, Simon C.

AU - Kyprianou, Andreas E.

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N1 - Funding Information: ∗Received by the editors January 7, 2021; accepted for publication (in revised form) January 4, 2022; published electronically June 30, 2022. https://doi.org/10.1137/21M1390578 Funding: This work was supported by EPSRC grant EP/P009220/1. †Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK (a.m.g.cox@bath.ac.uk a.kyprianou@bath.ac.uk). ‡Department of Statistics, University of Auckland, Auckland 1142, New Zealand (simon.harris@auckland.ac.nz). §School of Mathematical and Physical Sciences, University of Sussex, Brighton, BN1 9RH, UK (wangminmin03@ gmail.com). Publisher Copyright: © 2022 Society for Industrial and Applied Mathematics Publications. All rights reserved.

PY - 2022/12/31

Y1 - 2022/12/31

N2 - 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.

AB - 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.

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KW - Monte Carlo simulation

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JF - SIAM/ASA Journal on Uncertainty Quantification

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ER -

Monte-Carlo Methods for the Neutron Transport Equation

Abstract

Keywords

ASJC Scopus subject areas

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