Discontinuous Galerkin Methods for High-Dimensional Fokker-Planck Equations in Stochastic Dynamics

Abstract eng:
In this contribution, Discontinuous Galerkin methods are investgated as solution techniques for the high-dimensional Fokker-Planck equation (FPE). Time-Discontinuous Galerkin (TDG) methods are identified to provide stable solutions for smooth, as well as non-smooth functions. The TDG method allows for large time steps and are thus very efficient, at least for moderate dimensions. In higher dimensions, they become infeasible due to implicit coupling of the whole domain. For handling high-dimensional problems, spatial Discontinuous Galerkin (DG) methods are suggested, for their allowance of an element-wise split of the domain, and thus parallelization. The implementation of the Discontinuous Galerkin method for arbitrary dimensions is demonstrated.

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