TY - JOUR

T1 - Monte Carlo tracking drift-diffusion trajectories algorithm for solving narrow escape problems

AU - Sabelfeld, Karl K.

AU - Popov, Nikita

N1 - Publisher Copyright: © 2020 Walter de Gruyter GmbH, Berlin/Boston 2020. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - This study deals with a narrow escape problem, a well-know difficult problem of evaluating the probability for a diffusing particle to reach a small part of a boundary far away from the starting position of the particle. A direct simulation of the diffusion trajectories would take an enormous computer simulation time. Instead, we use a different approach which drastically improves the efficiency of the diffusion trajectory tracking algorithm by introducing an artificial drift velocity directed to the target position. The method can be efficiently applied to solve narrow escape problems for domains of long extension in one direction which is the case in many practical problems in biology and chemistry. The algorithm is meshless both in space and time, and is well applied to solve high-dimensional problems in complicated domains. We present in this paper a detailed numerical analysis of the method for the case of a rectangular parallelepiped. Both stationary and transient diffusion problems are handled.

AB - This study deals with a narrow escape problem, a well-know difficult problem of evaluating the probability for a diffusing particle to reach a small part of a boundary far away from the starting position of the particle. A direct simulation of the diffusion trajectories would take an enormous computer simulation time. Instead, we use a different approach which drastically improves the efficiency of the diffusion trajectory tracking algorithm by introducing an artificial drift velocity directed to the target position. The method can be efficiently applied to solve narrow escape problems for domains of long extension in one direction which is the case in many practical problems in biology and chemistry. The algorithm is meshless both in space and time, and is well applied to solve high-dimensional problems in complicated domains. We present in this paper a detailed numerical analysis of the method for the case of a rectangular parallelepiped. Both stationary and transient diffusion problems are handled.

KW - drift-diffusion trajectory

KW - first passage time

KW - Narrow escape problem

KW - random walk on spheres

UR - http://www.scopus.com/inward/record.url?scp=85089728639&partnerID=8YFLogxK

U2 - 10.1515/mcma-2020-2073

DO - 10.1515/mcma-2020-2073

M3 - Article

AN - SCOPUS:85089728639

VL - 26

SP - 177

EP - 191

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

SN - 0929-9629

IS - 3

ER -