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Volume 1, Issue 2
The Quadratic Collision Probability Method and the Importance Sampling Method in Monte Carlo Calculation for the Flux at a Point

Lu-Cheng Pei

J. Comp. Math., 1 (1983), pp. 161-169.

Published online: 1983-01

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  • Abstract

The unbounded estimate is one of the troublesome problems in Monte Carlo method. Particularly, in the calculation for the flux at a point, the estimate may approach infinite. In this paper, a collision probability method is proposed in Monte Carlo calculation for the flux at a point, and two kinds of methods with the bounded estimation are presented: the quadratic collision probability method and the importance sampling method. The former method is simple and easy to use, whereas the latter is suitable for calculation of flux at many different points simultaneously. The practical calculation indicates that the variance of the present methods can be reduced by about 50% and the efficiency can be increased by 2 to 4 time in comparison with the existing methods.  

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@Article{JCM-1-161, author = {Lu-Cheng Pei}, title = {The Quadratic Collision Probability Method and the Importance Sampling Method in Monte Carlo Calculation for the Flux at a Point}, journal = {Journal of Computational Mathematics}, year = {1983}, volume = {1}, number = {2}, pages = {161--169}, abstract = {

The unbounded estimate is one of the troublesome problems in Monte Carlo method. Particularly, in the calculation for the flux at a point, the estimate may approach infinite. In this paper, a collision probability method is proposed in Monte Carlo calculation for the flux at a point, and two kinds of methods with the bounded estimation are presented: the quadratic collision probability method and the importance sampling method. The former method is simple and easy to use, whereas the latter is suitable for calculation of flux at many different points simultaneously. The practical calculation indicates that the variance of the present methods can be reduced by about 50% and the efficiency can be increased by 2 to 4 time in comparison with the existing methods.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9692.html} }
TY - JOUR T1 - The Quadratic Collision Probability Method and the Importance Sampling Method in Monte Carlo Calculation for the Flux at a Point AU - Lu-Cheng Pei JO - Journal of Computational Mathematics VL - 2 SP - 161 EP - 169 PY - 1983 DA - 1983/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9692.html KW - AB -

The unbounded estimate is one of the troublesome problems in Monte Carlo method. Particularly, in the calculation for the flux at a point, the estimate may approach infinite. In this paper, a collision probability method is proposed in Monte Carlo calculation for the flux at a point, and two kinds of methods with the bounded estimation are presented: the quadratic collision probability method and the importance sampling method. The former method is simple and easy to use, whereas the latter is suitable for calculation of flux at many different points simultaneously. The practical calculation indicates that the variance of the present methods can be reduced by about 50% and the efficiency can be increased by 2 to 4 time in comparison with the existing methods.  

Lu-Cheng Pei. (1983). The Quadratic Collision Probability Method and the Importance Sampling Method in Monte Carlo Calculation for the Flux at a Point. Journal of Computational Mathematics. 1 (2). 161-169. doi:
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