TY - JOUR

T1 - First passage Monte Carlo algorithms for solving coupled systems of diffusion–reaction equations

AU - Karl, Sabelfeld

PY - 2019/2/1

Y1 - 2019/2/1

N2 - We suggest in this letter a new Random Walk on Spheres (RWS) stochastic algorithm for solving systems of coupled diffusion-reaction equations where the random walk is living both on the randomly walking spheres and inside the relevant balls. The method is mesh free both in space and time, and is well applied to solve high-dimensional problems with complicated domains. The algorithms are based on tracking the trajectories of the diffusing particles exactly in accordance with the probabilistic distributions derived from the explicit representation of the relevant Green functions for balls and spheres. They can be conveniently used not only for the solutions, but also for a direct calculation of fluxes to any part of the boundary without calculating the whole solution in the domain. Some applications to exciton flux calculations in the diffusion imaging method in semiconductors are discussed. (C) 2018 Elsevier Ltd. All rights reserved.

AB - We suggest in this letter a new Random Walk on Spheres (RWS) stochastic algorithm for solving systems of coupled diffusion-reaction equations where the random walk is living both on the randomly walking spheres and inside the relevant balls. The method is mesh free both in space and time, and is well applied to solve high-dimensional problems with complicated domains. The algorithms are based on tracking the trajectories of the diffusing particles exactly in accordance with the probabilistic distributions derived from the explicit representation of the relevant Green functions for balls and spheres. They can be conveniently used not only for the solutions, but also for a direct calculation of fluxes to any part of the boundary without calculating the whole solution in the domain. Some applications to exciton flux calculations in the diffusion imaging method in semiconductors are discussed. (C) 2018 Elsevier Ltd. All rights reserved.

KW - A system of diffusion–reaction equations

KW - Cathodoluminescence imaging of dislocations

KW - First passage time

KW - Random walk on spheres and balls

KW - A system of diffusion-reaction equations

UR - http://www.scopus.com/inward/record.url?scp=85053103386&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2018.08.018

DO - 10.1016/j.aml.2018.08.018

M3 - Article

AN - SCOPUS:85053103386

VL - 88

SP - 141

EP - 148

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

ER -