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

Sabelfeld Karl K. () and Popov Nikita ()
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Sabelfeld Karl K.: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentiev Str., 6, 630090Novosibirsk; and Novosibirsk State University, Pirogova str., 1, 630090 Novosibirsk, Russia
Popov Nikita: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentiev Str., 6, 630090Novosibirsk; and Novosibirsk State University, Pirogova str., 1, 630090 Novosibirsk, Russia

Monte Carlo Methods and Applications, 2020, vol. 26, issue 3, 177-191

Abstract: 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.

Keywords: Narrow escape problem; drift-diffusion trajectory; first passage time; random walk on spheres (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/mcma-2020-2073

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