Random walk on spheres method for solving drift-diffusion problems
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Karl K. Sabelfeld
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.
Funding source: Russian Science Foundation
Award Identifier / Grant number: 14-11-00083
Funding statement: Support of the Russian Science Foundation under Grant 14-11-00083 is kindly acknowledged.
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© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Random walk on spheres method for solving drift-diffusion problems
- On the construction of boundary preserving numerical schemes
- Perfect and ε-perfect simulation methods for the one-dimensional Kac equation
- Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the local times of the unknown process
- Improved Markov Chain Monte Carlo method for cryptanalysis substitution-transposition cipher
- The planar Couette flow with slip and jump boundary conditions in a microchannel
- A search for extensible low-WAFOM point sets
Articles in the same Issue
- Frontmatter
- Random walk on spheres method for solving drift-diffusion problems
- On the construction of boundary preserving numerical schemes
- Perfect and ε-perfect simulation methods for the one-dimensional Kac equation
- Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the local times of the unknown process
- Improved Markov Chain Monte Carlo method for cryptanalysis substitution-transposition cipher
- The planar Couette flow with slip and jump boundary conditions in a microchannel
- A search for extensible low-WAFOM point sets
