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The Numerical Approximation of Koopman Modes of a Nonlinear Operator Along a Trajectory

In: Sustained Simulation Performance 2017

Author

Listed:
  • Uwe Küster

    (High Performance Computing Center Stuttgart (HLRS))

  • Ralf Schneider

    (High Performance Computing Center Stuttgart (HLRS))

  • Andreas Ruopp

    (High Performance Computing Center Stuttgart (HLRS))

Abstract

The spectral theory of linear operators enables the analysis of their properties on stable subspaces. The Koopman operator allows to extend these approaches to a large class of nonlinear operators in a surprising way. This is even applicable for numerical analysis of time dependent data of simulations and measurements. We give here some remarks on the numerical approach, link it to spectral analysis by the Herglotz-Bochner theorem and are doing some steps for significance for partial differential equations.

Suggested Citation

  • Uwe Küster & Ralf Schneider & Andreas Ruopp, 2017. "The Numerical Approximation of Koopman Modes of a Nonlinear Operator Along a Trajectory," Springer Books, in: Michael M. Resch & Wolfgang Bez & Erich Focht & Michael Gienger & Hiroaki Kobayashi (ed.), Sustained Simulation Performance 2017, pages 27-51, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-66896-3_3
    DOI: 10.1007/978-3-319-66896-3_3
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