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Random walk on spheres algorithm for solving steady-state and transient diffusion-recombination problems

  • Irina Shalimova and Karl K. Sabelfeld ORCID logo EMAIL logo

Abstract

We further develop in this study the Random Walk on Spheres (RWS) stochastic algorithm for solving systems of coupled diffusion-recombination equations first suggested in our recent article [K. Sabelfeld, First passage Monte Carlo algorithms for solving coupled systems of diffusion–reaction equations, Appl. Math. Lett. 88 2019, 141–148]. The random walk on spheres process mimics the isotropic diffusion of two types of particles which may recombine to each other. Our motivation comes from the transport problems of free and bound exciton recombination. The algorithm is 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. Therefore, the method is mesh free both in space and time. In this paper we implement the RWS algorithm for solving the diffusion-recombination problems both in a steady-state and transient settings. Simulations are compared against the exact solutions. We show also how the RWS algorithm can be applied to calculate exciton flux to the boundary which provides the electron beam-induced current, the concentration of the survived excitons, and the cathodoluminescence intensity which are all integral characteristics of the solution to diffusion-recombination problem.

MSC 2010: 65C05; 65C40; 65Z05

Award Identifier / Grant number: 19-11-00019

Award Identifier / Grant number: 20-51-18009

Funding statement: This work is supported by the Russian Science Foundation under Grant No. 19-11-00019 in the part of the RWS algorithm development, and the RFBR and National Science Foundation of Bulgaria (NSFB), project number 20-51-18009, in the part of stochastic algorithms implementations.

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Received: 2021-05-02
Revised: 2021-10-08
Accepted: 2021-11-03
Published Online: 2021-11-04
Published in Print: 2021-12-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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