Journal of Scientific Computing

, Volume 61, Issue 3, pp 513–532 | Cite as

A Semi-Lagrangian Method for 3-D Fokker Planck Equations for Stochastic Dynamical Systems on the Sphere

  • A. RothEmail author
  • A. Klar
  • B. Simeon
  • E. Zharovsky


In this paper, we consider stochastic dynamical systems on the sphere and the associated Fokker–Planck equations. A semi-Lagrangian method combined with a Finite Volume discretization of the sphere is presented to solve the Fokker–Planck equation. The method is applied to a typical problem in fiber dynamics and textile production. The numerical results are compared to explicit solutions and Monte-Carlo solutions.


Fokker–Planck equation SDE Fiber lay-down Semi-Lagrange method Finite volume method 



This work has been supported by Deutsche Forschungsgemeinschaft (DFG), KL 1105/18-1 and by Bundesministerium für Bildung und Forschung (BMBF), Verbundprojekt OPAL.


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsTechnische Universität KaiserslauternKaiserslauternGermany
  2. 2.Fraunhofer ITWMKaiserslauternGermany

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