On average dimensions of particle transport estimators

Sobol Ilya M. () and Shukhman Boris V. ()
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Sobol Ilya M.: Keldysh Institute of Applied Mathematics, 4, Miusskaya sq., Moscow, 125047, Russia
Shukhman Boris V.: 1H-580 Place de la Fontaine, Montreal, QC, Canada

Monte Carlo Methods and Applications, 2018, vol. 24, issue 2, 147-151

Abstract: We considered average dimensions of the weighted Monte Carlo algorithm for a particle transport problem with multi-scattering setting and estimated the probability of particles penetration through a layer. The average dimension d^{\hat{d}} of the algorithm turned out to be small so that quasi-Monte Carlo estimates of the probability converge much faster than the Monte Carlo estimates. We justified the reasons to expect that the convergence of quasi-Monte Carlo estimates continue to be faster as the thickness of the layer increases. Here we calculated d^{\hat{d}} without the use of the ANOVA expansion.

Keywords: Monte Carlo methods (MC); weighted MC; quasi-MC; Sobol sequence; particle transport; average dimension; Owen’s formula (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:24:y:2018:i:2:p:147-151:n:7

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DOI: 10.1515/mcma-2018-0013

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