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

Author

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  • Sabelfeld Karl K.
  • Levykin Alexander I.

    (Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, NSU, Novosibirsk, Russia)

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.

Suggested Citation

  • Sabelfeld Karl K. & Levykin Alexander I., 2014. "A spectral method for isotropic diffusion equation with random concentration fluctuations of incoming flux of particles through circular-shaped boundaries," Monte Carlo Methods and Applications, De Gruyter, vol. 20(3), pages 173-180, September.
    • Handle: RePEc:bpj:mcmeap:v:20:y:2014:i:3:p:173-180:n:5
    DOI: 10.1515/mcma-2014-0001
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