A stochastic differential equation code for multidimensional Fokker-Planck type problems

Abstract

We present a newly developed numerical code that integrates Fokker–Planck type transport equations in four to six spatial dimensions (configuration plus momentum space) and time by means of stochastic differential equations. In contrast to other, similar approaches our code is not restricted to any special configuration or application, but is designed very generally with a modular structure and, moreover, allows for Cartesian, cylindrical or spherical coordinates. Depending on the physical application the code can integrate the equations forward or backward in time. We exemplify the mathematical ideas the method is based upon and describe the numerical realisation and implementation in detail. The code is validated for both cases against an established finite-differences explicit numerical code for a scenario that includes particle sources as well as a linear loss term. Finally we discuss the new possibilities opened up with respect to general applications and newly developed hardware.