TY - JOUR

T1 - Stochastic algorithm for solving transient diffusion equations with a precise accounting of reflection boundary conditions on a substrate surface

AU - Karl, Sabelfeld

N1 - Publisher Copyright: © 2019 Elsevier Ltd

PY - 2019/10/1

Y1 - 2019/10/1

N2 - A new random walk based stochastic algorithm for solving transient diffusion equations in domains where a reflection boundary condition is imposed on a plane part of the boundary is suggested. The motivation comes from the field of exciton transport and recombination in semiconductors where the reflecting boundary is the substrate plane surface while on the defects and dislocations an absorption boundary condition is prescribed. The idea of the method is based on the exact representations of the first passage time and position distributions on a parallelepiped (or a cube)with a reflection condition on its bed face lying on the substrate. The algorithm is meshfree both in space and time, the particle trajectories are moving inside the domain in accordance with the Random Walk on Spheres (RWS)process but when approaching the reflecting surface they switch to move on parallelepipeds (or cubes). The efficiency of the method is drastically increased compared with the standard RWS method. For illustration, we present an example of exciton flux calculations in the cathodoluminescence imaging method in semiconductors with a set of threading dislocations.

AB - A new random walk based stochastic algorithm for solving transient diffusion equations in domains where a reflection boundary condition is imposed on a plane part of the boundary is suggested. The motivation comes from the field of exciton transport and recombination in semiconductors where the reflecting boundary is the substrate plane surface while on the defects and dislocations an absorption boundary condition is prescribed. The idea of the method is based on the exact representations of the first passage time and position distributions on a parallelepiped (or a cube)with a reflection condition on its bed face lying on the substrate. The algorithm is meshfree both in space and time, the particle trajectories are moving inside the domain in accordance with the Random Walk on Spheres (RWS)process but when approaching the reflecting surface they switch to move on parallelepipeds (or cubes). The efficiency of the method is drastically increased compared with the standard RWS method. For illustration, we present an example of exciton flux calculations in the cathodoluminescence imaging method in semiconductors with a set of threading dislocations.

KW - Cathodoluminescence imaging of dislocations

KW - Diffusion–reaction equations

KW - First passage time

KW - Random walk on parallelepipeds

KW - Reflection boundary

KW - Diffusion-reaction equations

KW - RANDOM-WALK

UR - http://www.scopus.com/inward/record.url?scp=85065815552&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2019.05.003

DO - 10.1016/j.aml.2019.05.003

M3 - Article

AN - SCOPUS:85065815552

VL - 96

SP - 187

EP - 194

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

ER -