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

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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.

Original languageEnglish
Pages (from-to)131-146
Number of pages16
JournalMonte Carlo Methods and Applications
Volume25
Issue number2
DOIs
Publication statusPublished - 1 Jun 2019

Keywords

  • Anisotropic drift-diffusion-reaction equation
  • random walk on rectangles and parallelepipeds
  • stochastic expansion from cell to cell algorithm
  • transport of electrons and holes

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