Stochastic simulation algorithms for solving narrow escape diffusion problems by introducing a drift to the target

•A new meshless stochastic algorithm for solving narrow escape problems is developed.•The method drastically improves the efficiency of the conventional trajectory tracking methods.•Acceleration is achieved by introducing an artificial drift directed to the target position.•Simulations of exciton fl...

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Vydáno v:	Journal of computational physics Ročník 410; s. 109406
Hlavní autor:	Sabelfeld, Karl
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Cambridge Elsevier Inc 01.06.2020 Elsevier Science Ltd
Témata:	Algorithms Cathodoluminescence Cathodoluminescence imaging Computational physics Computer simulation Diffusion Domains Drift Drift-diffusion-reaction equations Electron beam induced current Excitons First passage time Fluxes Green's functions Mathematical analysis Meshless methods Narrow escape problems Random walk Random walk on spheres Reaction-diffusion equations Simulation Threading dislocations Tracking Narrow escape problems First passage time Cathodoluminescence imaging Drift-diffusion-reaction equations Random walk on spheres
ISSN:	0021-9991, 1090-2716
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Abstract	•A new meshless stochastic algorithm for solving narrow escape problems is developed.•The method drastically improves the efficiency of the conventional trajectory tracking methods.•Acceleration is achieved by introducing an artificial drift directed to the target position.•Simulations of exciton fluxes to dislocations in semiconductors are presented. We suggest in this paper a new stochastic simulation algorithm for solving narrow escape problems governed by drift-diffusion-reaction equations of high dimension. The developed method drastically improves the efficiency of the diffusion trajectory tracking algorithm by introducing an artificial drift directed to the target position. The method is especially appropriate to solve narrow escape problems for domains of very long extension in one direction which is the case in many practical problems. We present simulation results for a diffusion transport problem of calculation of cathodoluminescence intensity, a diffusion flux of excitons to a threading dislocation, and the electron beam induced current in a semiconductor. The diffusion tracking algorithm is based on the random walk on spheres process. The method is meshless both in space and time, and is well applied to solve high-dimensional problems in 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. 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.
AbstractList	•A new meshless stochastic algorithm for solving narrow escape problems is developed.•The method drastically improves the efficiency of the conventional trajectory tracking methods.•Acceleration is achieved by introducing an artificial drift directed to the target position.•Simulations of exciton fluxes to dislocations in semiconductors are presented. We suggest in this paper a new stochastic simulation algorithm for solving narrow escape problems governed by drift-diffusion-reaction equations of high dimension. The developed method drastically improves the efficiency of the diffusion trajectory tracking algorithm by introducing an artificial drift directed to the target position. The method is especially appropriate to solve narrow escape problems for domains of very long extension in one direction which is the case in many practical problems. We present simulation results for a diffusion transport problem of calculation of cathodoluminescence intensity, a diffusion flux of excitons to a threading dislocation, and the electron beam induced current in a semiconductor. The diffusion tracking algorithm is based on the random walk on spheres process. The method is meshless both in space and time, and is well applied to solve high-dimensional problems in 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. 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. We suggest in this paper a new stochastic simulation algorithm for solving narrow escape problems governed by drift-diffusion-reaction equations of high dimension. The developed method drastically improves the efficiency of the diffusion trajectory tracking algorithm by introducing an artificial drift directed to the target position. The method is especially appropriate to solve narrow escape problems for domains of very long extension in one direction which is the case in many practical problems. We present simulation results for a diffusion transport problem of calculation of cathodoluminescence intensity, a diffusion flux of excitons to a threading dislocation, and the electron beam induced current in a semiconductor. The diffusion tracking algorithm is based on the random walk on spheres process. The method is meshless both in space and time, and is well applied to solve high-dimensional problems in 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. 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.
ArticleNumber	109406
Author	Sabelfeld, Karl
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Cites_doi	10.1137/15M1019258 10.1016/j.matcom.2011.10.008 10.1016/j.cpc.2014.10.007 10.1515/156939603322601969 10.1073/pnas.0706599104 10.1016/j.physleta.2008.02.076 10.1080/00207215708937106 10.1063/1.5022170 10.1016/j.cpc.2015.07.014 10.1023/A:1002701813926 10.1515/mcma-2019-2039 10.1016/S0010-4655(01)00144-8 10.1137/070705039 10.1103/PhysRevE.84.031129 10.1002/nme.1620100507 10.1103/PhysRevApplied.12.054038 10.1006/jmra.1993.1056 10.1016/j.cpc.2019.01.013 10.1103/PhysRevLett.107.017402 10.1016/j.commatsci.2013.11.019 10.1515/mcma-2016-0118 10.1016/j.jcp.2017.10.058 10.1007/s40820-019-0245-5 10.1007/s10955-016-1691-9 10.1007/BF01060076 10.1007/s00285-015-0955-3 10.1063/1.3160546 10.1515/mcma-2017-0113 10.1016/j.agrformet.2004.07.007 10.1063/1.2746840 10.1016/j.cpc.2019.04.001
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Keywords	Narrow escape problems First passage time Cathodoluminescence imaging Drift-diffusion-reaction equations Random walk on spheres
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Snippet	•A new meshless stochastic algorithm for solving narrow escape problems is developed.•The method drastically improves the efficiency of the conventional... We suggest in this paper a new stochastic simulation algorithm for solving narrow escape problems governed by drift-diffusion-reaction equations of high...
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SubjectTerms	Algorithms Cathodoluminescence Cathodoluminescence imaging Computational physics Computer simulation Diffusion Domains Drift Drift-diffusion-reaction equations Electron beam induced current Excitons First passage time Fluxes Green's functions Mathematical analysis Meshless methods Narrow escape problems Random walk Random walk on spheres Reaction-diffusion equations Simulation Threading dislocations Tracking
Title	Stochastic simulation algorithms for solving narrow escape diffusion problems by introducing a drift to the target
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