TY - JOUR

T1 - Random walk on rectangles and parallelepipeds algorithm for solving transient anisotropic drift-diffusion-reaction problems

AU - Sabelfeld, Karl K.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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.

AB - 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.

KW - Anisotropic drift-diffusion-reaction equation

KW - random walk on rectangles and parallelepipeds

KW - stochastic expansion from cell to cell algorithm

KW - transport of electrons and holes

UR - http://www.scopus.com/inward/record.url?scp=85065676191&partnerID=8YFLogxK

U2 - 10.1515/mcma-2019-2039

DO - 10.1515/mcma-2019-2039

M3 - Article

AN - SCOPUS:85065676191

VL - 25

SP - 131

EP - 146

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

SN - 0929-9629

IS - 2

ER -