TY - JOUR

T1 - On the efficiency of using correlative randomized algorithms for solving problems of gamma radiation transfer in stochastic medium

AU - Medvedev, Ilia N.

N1 - Publisher Copyright: © 2022 Walter de Gruyter GmbH, Berlin/Boston.

PY - 2022/8/1

Y1 - 2022/8/1

N2 - To solve problems of radiation balance, optical sounding, and tomography, it may be necessary to take into account multiple scattering of radiation in a stochastically inhomogeneous medium. In real radiation models, for this purpose, the numerical-statistical 'majorant cross-section method' (MCM, delta-Woodcock tracking) is used based on the alignment of the optical density field by adding an artificial 'delta scattering' event. However, the computation cost of the corresponding unbiased estimate of the averaged problem solution infinitely increases as the correlation scale (correlation radius L) of standard mosaic models for a random medium density decreases. Previously, we constructed the MCM randomization providing asymptotically (for L → 0) unbiased estimates of the required functionals, in which the value of the physical attenuation coefficient is randomly chosen at the end of the particle free path l under condition l > L. Otherwise the value of the physical attenuation coefficient is the same as at the starting point of the particle (CR algorithm). In a more accurate functional correlative randomized algorithm (FCR algorithm), the coefficient remains the same with a probability determined by the correlation function. These correlative randomized algorithms were implemented for a mixture of homogeneous substance (water) and a Poisson ensemble of 'empty' balls. In the present paper, we construct correlative randomized algorithms for problems related to transfer through a 'thick' layer containing a water and a Poisson ensemble of 'empty' layers. A detailed comparative analysis of the results obtained by exact direct simulation (MCM) and approximate algorithms (CR, FCR) for the problems of gamma radiation transfer through a 'thick' water layer containing a Poisson ensemble of 'empty' layers or balls is presented.

AB - To solve problems of radiation balance, optical sounding, and tomography, it may be necessary to take into account multiple scattering of radiation in a stochastically inhomogeneous medium. In real radiation models, for this purpose, the numerical-statistical 'majorant cross-section method' (MCM, delta-Woodcock tracking) is used based on the alignment of the optical density field by adding an artificial 'delta scattering' event. However, the computation cost of the corresponding unbiased estimate of the averaged problem solution infinitely increases as the correlation scale (correlation radius L) of standard mosaic models for a random medium density decreases. Previously, we constructed the MCM randomization providing asymptotically (for L → 0) unbiased estimates of the required functionals, in which the value of the physical attenuation coefficient is randomly chosen at the end of the particle free path l under condition l > L. Otherwise the value of the physical attenuation coefficient is the same as at the starting point of the particle (CR algorithm). In a more accurate functional correlative randomized algorithm (FCR algorithm), the coefficient remains the same with a probability determined by the correlation function. These correlative randomized algorithms were implemented for a mixture of homogeneous substance (water) and a Poisson ensemble of 'empty' balls. In the present paper, we construct correlative randomized algorithms for problems related to transfer through a 'thick' layer containing a water and a Poisson ensemble of 'empty' layers. A detailed comparative analysis of the results obtained by exact direct simulation (MCM) and approximate algorithms (CR, FCR) for the problems of gamma radiation transfer through a 'thick' water layer containing a Poisson ensemble of 'empty' layers or balls is presented.

KW - computation cost

KW - correlative-randomized algorithm

KW - direct simulation

KW - estimation error

KW - gamma radiation transfer

KW - majorant cross-section method (delta-Woodcock tracking)

KW - Poisson point process

KW - random set of layers (balls)

KW - Stochastic medium

UR - http://www.scopus.com/inward/record.url?scp=85137714650&partnerID=8YFLogxK

U2 - 10.1515/rnam-2022-0020

DO - 10.1515/rnam-2022-0020

M3 - Article

AN - SCOPUS:85137714650

VL - 37

SP - 231

EP - 240

JO - Russian Journal of Numerical Analysis and Mathematical Modelling

JF - Russian Journal of Numerical Analysis and Mathematical Modelling

SN - 0927-6467

IS - 4

ER -