International Conference «Mathematical and Informational Technologies, MIT-2013»
(X Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, September, 5–8, 2013

Budva, Montenegro, September, 9-14, 2013

Zhuplev A.   Prokhorov I.  

Maximum cross-section algorithms in the Monte Carlo method for solving of transport equation

Reporter: Prokhorov I.

The numerical solution questions of the boundary problem for the stationary radiation transport equation in a three-dimensional domain filled with heterogeneous nonmultiplying material was considered.
Three Monte Carlo methods were researched. All methods are based on the summing up of the Neumann series for the solution of the transport equation. The first two implementations are modifications of the maximum cross-section method. The first one is classical, the second is method using  branching Markov chains, which allows to reduce the estimate dispersion for the sum of the Neumann series. The third implementation is based on proposition of piecewise constant cross-section of interaction of the radiation with media. The theoretical justification for the rate of convergence of the Neumann series for the solution of the transport equation was given.  Series of experiments for the domains with spherical inclusions for isotropic scattering and "forward scattering"  for a different number of trajectories and the members of the Neumann series were conducted. Also the dispersion error    and laboriousness of each method are calculated. Effectiveness of the methods was investigated. Recommendations for the application of each of methods are given.  Analysis of findings by comparison with the results of other authors was also provided.

Abstracts file: Zhuplev_AS.doc

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