Abstract:
The new algorithms of statistical modeling of radiative transfer through different types of stochastic homogeneous isotropic media have been created. To this end a special geometric implementation of “the maximum cross-section method” has been developed. This implementation allows one to take into account the radiation absorption by the exponential multiplier factor. The dependence of a certain class of solution functionals of the radiative transfer equation on the correlation length and the field type is studied theoretically and by means of numerical experiments. The theorem about the convergence of these functionals to the corresponding functionals for an average field with decreasing the correlation length up to zero has been proved.
Key words:
Poisson ensemble, random field, correlation function, radiative transfer, maximum cross-section method.
This publication is cited in the following 12 articles:
G. A. Mikhailov, I. N. Medvedev, “New Computer Efficient Approximations of Random Functions for Solving Stochastic Transport Problems”, Comput. Math. and Math. Phys., 64:2 (2024), 314
G. A. Mikhailov, G. Z. Lotova, I. N. Medvedev, “Effektivno realizuemye priblizhennye modeli sluchainykh funktsii v stokhasticheskikh zadachakh teorii perenosa chastits”, Sib. zhurn. vychisl. matem., 27:2 (2024), 189–209
G. A. Mikhailov, G. Z. Lotova, I. N. Medvedev, “Efficiently Realized Approximate Models of Random Functions in Stochastic Problems of the Theory of Particle Transfer”, Numer. Analys. Appl., 17:2 (2024), 152
G. Z. Lotova, G. A. Mikhailov, S. A. Rozhenko, “Optimization of a Numerical-Statistical Algorithm for Estimating the Mean Particle Flow in a Bounded Random Medium with Multiplication”, Comput. Math. and Math. Phys., 64:11 (2024), 2705
G. A. Mikhailov, “Randomized algorithms of Monte Carlo method for problems with random parameters (“double randomization” method)”, Num. Anal. Appl., 12:2 (2019), 155–165
G. A. Mikhailov, “Improvement of multidimensional randomized Monte Carlo algorithms with “splitting””, Comput. Math. Math. Phys., 59:5 (2019), 775–781
A. Yu. Ambos, G. A. Mikhailov, “Estimation by Monte Carlo method of functional characteristics of the radiation intensity field passing throw a random medium”, Num. Anal. Appl., 11:4 (2018), 279–292
G. A. Mikhailov, G. Z. Lotova, “Monte Carlo methods for estimating the probability distributions of criticality parameters of particle transport in a randomly perturbed medium”, Comput. Math. Math. Phys., 58:11 (2018), 1828–1837
G. A. Mikhailov, “Optimization of randomized Monte Carlo algorithms for solving problems with random parameters”, Dokl. Math., 98:2 (2018), 448–451
A. Yu. Ambos, G. A. Mikhailov, “Numerically statistical simulation of the intensity field of the radiation transmitted through a random medium”, Russ. J. Numer. Anal. Math. Model, 33:3 (2018), 161–171
G. A. Mikhailov, G. Z. Lotova, “New Monte Carlo algorithms for estimating probability moments of criticality parameters for a scattering process with multiplication in stochastic media”, Dokl. Math., 97:1 (2018), 6–10
A. Yu. Ambos, G. Lotova, G. Mikhailov, “New Monte Carlo algorithms for investigation of criticality fluctuations in the particle scattering process with multiplication in stochastic media”, Russ. J. Numer. Anal. Math. Model, 32:3 (2017), 165–172
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