A spectral method for isotropic diffusion equation with random concentration fluctuations of incoming flux of particles through circular-shaped boundaries

Sabelfeld Karl K. () and Levykin Alexander I. ()
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Sabelfeld Karl K.: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, NSU, Novosibirsk, Russia
Levykin Alexander I.: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, NSU, Novosibirsk, Russia

Monte Carlo Methods and Applications, 2014, vol. 20, issue 3, 173-180

Abstract: We present in this paper a further development of the stochastic spectral method for solving boundary value problems in domains which are composed by a set of overlapped discs first suggested by the first author in Appl. Math. Comput. 219 (2013), no. 10, 5123–5139]. We study statistical characteristics of the solution to isotropic diffusion problem in response to fluctuating incoming flux of particles through the circular-shaped boundaries. Performance of the method is illustrated by a series of numerical experiments. The method can be considered as a direct inversion of the integral Poisson formula representing the solution in the disc, so it is highly accurate and fast for the class of domains considered. This makes possible to solve an ensemble of equations with random samples of boundary conditions and calculate the desired statistical characteristics.

Keywords: Fluctuation-induced kinetics; isotropic diffusion; spectral method; Poisson integral formula; circular-shaped boundaries (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1515/mcma-2014-0001

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