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Aspects on Data Analysis and Visualization for Complicated Dynamical Systems

In: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

Author

Listed:
  • J. Becker

    (Universität Freiburg, Mathematische Fakultät)

  • D. Bürkle

    (Universität Freiburg, Institut für Angewandte Mathematik)

  • R.-T. Happe

    (Universität Freiburg, Mathematische Fakultät)

  • T. Preußer

    (Universität Bonn, Institut für Angewandte Mathematik)

  • M. Rumpf

    (Universität Bonn, Institut für Angewandte Mathematik)

  • M. Spielberg

    (Universität Bonn, Institut für Angewandte Mathematik)

  • R. Strzodka

    (Universität Bonn, Institut für Angewandte Mathematik)

Abstract

Flow visualization is an indispensible tool for the understandig of complex flow phenomena in computational fluid dynamics and the analysis of dynamical systems. In this note we will present several ways for an effective post processing of fluid flows and flows on invariant manifolds of dynamical systems. Feature extraction techniques will be present which reduce the informational content of large timedependent data sets to its mainly intersesting essence. Futhermore, we present visualization approaches which are based on partial differential equations. Similar to the modelling of physical phenomena by partial differential equations, in the postprocessing of data such equations naturally arise as well. Finally, the method for the dense covering of an invariant manifold with streamlines is outlined, which enables us to represent the geometry of the objects, statistical information on it, and the local flow properties at the same time.

Suggested Citation

  • J. Becker & D. Bürkle & R.-T. Happe & T. Preußer & M. Rumpf & M. Spielberg & R. Strzodka, 2001. "Aspects on Data Analysis and Visualization for Complicated Dynamical Systems," Springer Books, in: Bernold Fiedler (ed.), Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pages 417-430, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56589-2_18
    DOI: 10.1007/978-3-642-56589-2_18
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