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Random walk on rectangles and parallelepipeds algorithm for solving transient anisotropic drift-diffusion-reaction problems

Author

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  • Sabelfeld Karl K.

    (Institute of Computational Mathematics and Mathematical Geophysics, and Novosibirsk State University, Novosibirsk, Russia)

Abstract

In this paper a random walk on arbitrary rectangles (2D) and parallelepipeds (3D) algorithm is developed for solving transient anisotropic drift-diffusion-reaction equations. The method is meshless, both in space and time. The approach is based on a rigorous representation of the first passage time and exit point distributions for arbitrary rectangles and parallelepipeds. The probabilistic representation is then transformed to a form convenient for stochastic simulation. The method can be used to calculate fluxes to any desired part of the boundary, from arbitrary sources. A global version of the method we call here as a stochastic expansion from cell to cell (SECC) algorithm for calculating the whole solution field is suggested. Application of this method to solve a system of transport equations for electrons and holes in a semicoductor is discussed. This system consists of the continuity equations for particle densities and a Poisson equation for electrostatic potential. To validate the method we have derived a series of exact solutions of the drift-diffusion-reaction problem in a three-dimensional layer presented in the last section in details.

Suggested Citation

  • Sabelfeld Karl K., 2019. "Random walk on rectangles and parallelepipeds algorithm for solving transient anisotropic drift-diffusion-reaction problems," Monte Carlo Methods and Applications, De Gruyter, vol. 25(2), pages 131-146, June.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:2:p:131-146:n:7
    DOI: 10.1515/mcma-2019-2039
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