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EP: Fachverband Extraterrestrische Physik
EP 4: Numerische Modellierung
EP 4.5: Vortrag
Dienstag, 13. März 2012, 18:00–18:15, V55.02
New Perspectives on Numerics for Stochastic Differential Equations and their Application to Energetic Particle Transport — •Frederic Effenberger1, Horst Fichtner1, Ingo Büsching1, Andreas Kopp2, and Robin Stern1 — 1Ruhr-Universität Bochum, Bochum, Germany — 2Christian-Albrechts-Universität zu Kiel, Kiel, Germany
During the last decade Stochastic Differential Equations (SDEs) have become a viable numerical tool in space physics, in particular for the modeling of Cosmic Ray (CR) transport processes. Their application ranges from detailed calculations of solar energetic particle events to the CR transport in the Heliosphere and in the Galaxy. At the heart of the applicability of SDEs to CR diffusion is the fundamental equivalency between the parabolic Fokker-Planck type transport equation and SDEs involving Wiener processes to represent the stochastic Brownian motion of pseudo particles (phase space elements). In recent years, this equivalency has been extended to more general anomalous diffusion processes with different scalings between temporal and spatial displacements, leading to Fokker-Planck equations of fractional order and generalized probability distributions in the respective SDEs. We will present numerical tests and applications of this approach to anomalous diffusion, concerning the fractional derivatives in the Fokker-Planck equations as well as the equivalent formulation with SDEs, including technical aspects like the speedup by using graphic processing units (GPUs).