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Mapping the Arnold web with a graphic processing unit.

A Seibert1, S Denisov, A V Ponomarev

  • 1Institute of Physics, University of Augsburg, Universitätstr.1, D-86159 Augsburg, Germany. armin.seibert@physik.uni-augsburg.de

Chaos (Woodbury, N.Y.)
|January 10, 2012
PubMed
Summary
This summary is machine-generated.

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Arnold diffusion, a phenomenon in Hamiltonian systems, is explored faster using GPU-supercomputers. This method significantly speeds up mapping the Arnold web, a complex structure crucial for understanding system dynamics.

Area of Science:

  • Dynamical systems
  • Statistical mechanics
  • Computational physics

Background:

  • Arnold diffusion is a dynamical phenomenon in non-integrable Hamiltonian systems with M ≥ 3 degrees of freedom.
  • This diffusion occurs through a web of resonance channels, enabling exploration of the entire energy shell.
  • Mapping the Arnold web is computationally intensive due to the slow nature of Arnold diffusion.

Purpose of the Study:

  • To investigate the efficiency of graphic processing unit (GPU)-supercomputers for exploring the Arnold web.
  • To determine the potential speedup of GPU-based simulations compared to traditional CPU-based methods for mapping Arnold diffusion.

Main Methods:

  • Simulations of Hamiltonian systems were performed using graphic processing unit (GPU)-supercomputers.

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  • The performance of GPU-based simulations was compared against standard CPU-based simulations.
  • The time-consuming task of mapping the Arnold web was analyzed.

    • Main Results:

    • GPU-supercomputer exploration of the Arnold web resulted in significant speedups.
    • Speedups of two orders of magnitude were achieved compared to CPU-based simulations.
    • This demonstrates the efficacy of GPU acceleration for studying Arnold diffusion.

    Conclusions:

    • Graphic processing unit (GPU)-supercomputers offer a substantial acceleration for mapping the Arnold web.
    • The use of GPU technology can overcome the time-consuming limitations of studying Arnold diffusion.
    • Accelerated exploration of the Arnold web facilitates a deeper understanding of Hamiltonian system dynamics.