On the efficiency of using correlative randomized algorithms for solving problems of gamma radiation transfer in stochastic medium
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Ilia N. Medvedev
Abstract
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.
Funding statement: The study was carried out under state contract with ICMMG SB RAS No. 0251-2021-0002.
Acknowledgment
The author expresses his gratitude to the staff of the Laboratory of Monte Carlo Methods of the ICM&MG, SB RAS, namely, to Corresponding member of RAS G. A. Mikhailov and Ph.D. G. Lotova for useful advice and comments.
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Articles in the same Issue
- Frontmatter
- Glacier parameterization in SLAV numerical weather prediction model
- Optimal disturbances for periodic solutions of time-delay differential equations
- Construction and optimization of numerically-statistical projection algorithms for solving integral equations
- Linear regularized finite difference scheme for the quasilinear subdiffusion equation
- On the efficiency of using correlative randomized algorithms for solving problems of gamma radiation transfer in stochastic medium
- Error identities for the reaction–convection–diffusion problem and applications to a posteriori error control
Articles in the same Issue
- Frontmatter
- Glacier parameterization in SLAV numerical weather prediction model
- Optimal disturbances for periodic solutions of time-delay differential equations
- Construction and optimization of numerically-statistical projection algorithms for solving integral equations
- Linear regularized finite difference scheme for the quasilinear subdiffusion equation
- On the efficiency of using correlative randomized algorithms for solving problems of gamma radiation transfer in stochastic medium
- Error identities for the reaction–convection–diffusion problem and applications to a posteriori error control
