Research output: Contribution to journal › Article › peer-review
Random walk on rectangles and parallelepipeds algorithm for solving transient anisotropic drift-diffusion-reaction problems. / Sabelfeld, Karl K.
In: Monte Carlo Methods and Applications, Vol. 25, No. 2, 01.06.2019, p. 131-146.Research output: Contribution to journal › Article › peer-review
}
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 -
ID: 20049327