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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2014, 19(2), 134-143;

Simplified, Analytically Solvable Model Problem for Non-Analog Monte Carlo Methods

Department of Radiation Oncology, Akdeniz University, 07058, Kampüs, Antalya, Turkey
Department of Nuclear Energy Engineering, Hacettepe University, 06532, Beytepe, Ankara, Turkey
Authors to whom correspondence should be addressed.
Published: 1 August 2014
PDF [276 KB, uploaded 1 March 2016]


In Monte Carlo particle transport, it is important to change the variance of calculations of relatively rare events with a technique known as non-analog Monte Carlo. In order to reduce the variance and the computation time, biasing techniques are introduced to accelerate the calculation convergence without changing the outcome. However these variance reduction techniques are often complex and can only be solved by computer codes. In this study, a simplified, analytically solvable model problem is introduced for non-analog Monte Carlo methods. A sample problem for neutrons passing through a thick shield is simulated. The drawback of this simulation is the expensive computation time and large variance for analog Monte Carlo methods. So, biasing techniques like implicit capture and splitting are introduced and the problem is solved analytically.
Keywords: non-analog Monte Carlo; variance reduction; neutron transport non-analog Monte Carlo; variance reduction; neutron transport
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Çeçen, Y.; Tombakoğlu, M. Simplified, Analytically Solvable Model Problem for Non-Analog Monte Carlo Methods. Math. Comput. Appl. 2014, 19, 134-143.

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