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Algorithms for Forward and Backward Solution of the Fokker-Planck Equation in the Heliospheric Transport of Cosmic Rays

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Parallel Processing and Applied Mathematics (PPAM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10777))

Abstract

Motion of charged particles in an inhomogeneous turbulent medium as magnetic field is described by partial differential equations of the Fokker-Planck-Kolmogorov type. We present an algorithm of numerical solution of the four-dimensional Fokker-Planck equation in three-dimensional spherical coordinates system. The algorithm is based on Monte Carlo simulations of the stochastic motion of quasi-particles guided by the set of stochastic differential equations corresponding to the Fokker-Planck equation by the Ito formalism. We present the parallel algorithm in Julia programming language. We simulate the transport of cosmic rays in the heliosphere considering the full three-dimensional diffusion tensor. We compare forward- and backward-in-time solutions of the transport equation and discuss its computational advantages and disadvantages.

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Acknowledgments

This work is supported by The Polish National Science Centre grant awarded by decision number DEC-2012/07/D/ST6/02488. Calculations were performed at the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM) at Warsaw University within the computational grant no. G66-19.

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Authors and Affiliations

  1. Institute of Computer Sciences, Siedlce University, Siedlce, Poland

    Anna Wawrzynczak

  2. Institute of Mathematics and Physics, Siedlce University, Siedlce, Poland

    Renata Modzelewska & Agnieszka Gil

Authors
  1. Anna Wawrzynczak
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  2. Renata Modzelewska
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  3. Agnieszka Gil
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Corresponding author

Correspondence to Anna Wawrzynczak .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  3. University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Wawrzynczak, A., Modzelewska, R., Gil, A. (2018). Algorithms for Forward and Backward Solution of the Fokker-Planck Equation in the Heliospheric Transport of Cosmic Rays. In: Wyrzykowski, R., Dongarra, J., Deelman, E., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2017. Lecture Notes in Computer Science(), vol 10777. Springer, Cham. https://doi.org/10.1007/978-3-319-78024-5_2

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  • DOI: https://doi.org/10.1007/978-3-319-78024-5_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78023-8

  • Online ISBN: 978-3-319-78024-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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