Adaptive Monte Carlo Algorithms for General Transport Problems

Jerome Spanier (), Rong Kong and Martin Ambrose
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Jerome Spanier: University of California, Irvine, Beckman Laser Institute

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, pp 467-483 from Springer

Abstract: Abstract Recently there has been a concerted effort to develop adaptively modified Monte Carlo algorithms that converge geometrically to solutions of the radiative transport equation. We have concentrated on algorithms that extend to integral equations methods first proposed for matrix equations by Halton in 1962 [Halton, J., Proc. Camb. Phil. Soc., 58, 57–78 (1962)]. Geometric convergence has been rigorously demonstrated [Kong, R., and Spanier, J., J. Comp. Phys., 227(23), 9762–9777 (2008)] for these “first generation” (G1) algorithms but their practical utility is limited by computational complexities resulting from the expansion. Recently, we have developed new adaptive algorithms that overcome most of the computational restrictions of the earlier algorithms and we have also established the geometric convergence of these “second generation” (G2) algorithms [Kong, R. and Spanier, J.: Geometric convergence of second generation adaptive Monte Carlo algorithms for general transport problems based on sequential correlated sampling. In review]. In this paper we outline the main ideas involved and indicate how the resulting G2 algorithm might be optimized using information drawn from simulations of both the RTE and the dual RTE. Simple examples will illustrate these ideas and the gains in computational efficiency that the new methods can achieve.

Keywords: Phase Space; Monte Carlo; Adaptive Algorithm; Importance Sampling; Variance Reduction (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04107-5_30

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DOI: 10.1007/978-3-642-04107-5_30

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