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Solving Ordinary Differential Equations on GPUs

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Book cover Numerical Computations with GPUs

Abstract

Ordinary Differential Equations (ODEs) are a fundamental mathematical tool to model physical, biological or chemical systems, and they are widely used in engineering, economics and social sciences. Given their vast appearance, it is of crucial importance to develop efficient numerical routines for solving ODEs that employ the computational power of modern GPUs. Here, we present a high-level approach to compute numerical solutions of ODEs by developing a generic implementation of the most common algorithms and combining this with modern C\(++\) libraries like VexCL and Thrust. Our approach is based on generic programming and results in highly scalable and easy-to-use source code.

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Notes

  1. 1.

    http://www.odeint.com.

  2. 2.

    http://thrust.github.com.

  3. 3.

    http://www.simunova.com/gpu_mtl4.

  4. 4.

    https://github.com/ddemidov/vexcl.

  5. 5.

    http://viennacl.sourceforge.net/.

  6. 6.

    https://github.com/kylelutz/compute.

  7. 7.

    In Mathematics, the independent variable is often called x and the function is y(x).

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Acknowledgements

This work has been partially supported by the Russian Foundation for Basic Research (RFBR) grants No. 12-07-0007, 12-01-00333a, and by the Russian Government Program of Competitive Growth of Kazan Federal University. M. M. thankfully acknowledges financial support through the visitors program of the MPIPKS, Dresden (Germany).

Author information

Authors and Affiliations

  1. Ambrosys GmbH, Albert-Einstein-Str. 1-5, 14469, Potsdam, Germany

    Karsten Ahnert

  2. Kazan Branch of Joint Supercomputer Center, Russian Academy of Sciences, Lobachevsky st. 2/31, 420011, Kazan, Russia

    Denis Demidov

  3. Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187, Dresden, Germany

    Mario Mulansky

  4. TU-Dresden, Institute for Theoretical Physics, Zellescher Weg 17, 01069, Dresden, Germany

    Mario Mulansky

Authors
  1. Karsten Ahnert
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  2. Denis Demidov
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  3. Mario Mulansky
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Corresponding author

Correspondence to Karsten Ahnert .

Editor information

Editors and Affiliations

  1. National Center for Supercomputing Applications, University of Illinois, Urbana, Illinois, USA

    Volodymyr Kindratenko

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Ahnert, K., Demidov, D., Mulansky, M. (2014). Solving Ordinary Differential Equations on GPUs. In: Kindratenko, V. (eds) Numerical Computations with GPUs. Springer, Cham. https://doi.org/10.1007/978-3-319-06548-9_7

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  • DOI: https://doi.org/10.1007/978-3-319-06548-9_7

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