Random walk on spheres method for solving drift-diffusion problems

Sabelfeld Karl K. ()
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Sabelfeld Karl K.: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia

Monte Carlo Methods and Applications, 2016, vol. 22, issue 4, 265-275

Abstract: The well-known random walk on spheres method (RWS) for the Laplace equation is here extended to drift-diffusion problems. First we derive a generalized spherical mean value relation which is an extension of the classical integral mean value relation for the Laplace equation. Next we give a probabilistic interpretation of the kernel. The distribution on the sphere generated by this kernel is then related to the von Mises–Fisher distribution on the sphere which can be efficiently simulated. The rigorous expressions are given for the case of constant velocity drift, but the algorithm is then extended to solve drift-diffusion problems with arbitrary varying drift velocity vector. Applications to cathodoluminescence and EBIC imaging of defects and dislocations in semiconductors are discussed.

Keywords: Drift-diffusion equation; von Mises–Fisher distribution; spherical mean value relation; Robin boundary conditions; cathodoluminescence (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1515/mcma-2016-0118

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