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000859038 1001_ $$0P:(DE-Juel1)5017$$aReiser, D.$$b0$$eCorresponding author
000859038 245__ $$aOn the possibility of track length based Monte-Carlo algorithms for stationary drift-diffusion systems with sources and sinks
000859038 260__ $$aAmsterdam$$bElsevier$$c2019
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000859038 520__ $$aThe problem of constructing Monte-Carlo solutions of drift-diffusion systems corresponding to Fokker–Planck equations with sources and sinks is revisited. Firstly, a compact formalism is introduced for the specific problem of stationary solutions. This leads to identification of the dwell time as the key quantity to characterize the system and to obtain a proper normalization for statistical analysis of numerical results. Secondly, the question of appropriate track length estimators for drift-diffusion systems is discussed for a 1D model system. It is found that a simple track length estimator can be given only for pure drift motion without diffusion. The stochastic nature of the diffusive part cannot be appropriately described by the path length of simulation particles. Further analysis of the usual situation with inhomogeneous drift and diffusion coefficients leads to an error estimate based on particle trajectories. The result for limits in grid cell size and time step used for the construction of Monte-Carlo trajectories resembles the Courant-Friedrichs-Lewy and von Neumann conditions for explicit methods.
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000859038 7001_ $$0P:(DE-Juel1)165905$$aRomazanov, J.$$b1$$ufzj
000859038 7001_ $$0P:(DE-Juel1)157640$$aLinsmeier, Ch.$$b2
000859038 773__ $$0PERI:(DE-600)1469164-4$$a10.1016/j.jcp.2018.07.051$$gVol. 377, p. 219 - 231$$p219 - 231$$tJournal of computational physics$$v377$$x0021-9991$$y2019
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