Parallel algorithms for the determination of lyapunov characteristics of large nonlinear dynamical systems

  • Authors:

  • Günter Radons;Gudula Rünger;Michael Schwind;Hong-liu Yang

  • Affiliations:

  • Institute of Physics, Technical University Chemnitz, Chemnitz, Germany;Department of Computer Science, Technical University Chemnitz, Chemnitz, Germany;Department of Computer Science, Technical University Chemnitz, Chemnitz, Germany;Institute of Physics, Technical University Chemnitz, Chemnitz, Germany

  • Venue:
  • PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
  • Year:
  • 2004

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Abstract

Lyapunov vectors and exponents are of great importance for understanding the dynamics of many-particle systems. We present results of performance tests on different processor architectures of several parallel implementations for the calculation of all Lyapunov characteristics. For the most time consuming reorthogonalization steps, which have to be combined with molecular dynamics simulations, we tested different parallel versions of the Gram-Schmidt algorithm and of QR-decomposition. The latter gave the best results with respect to runtime and stability. For large systems the blockwise parallel Gram-Schmidt algorithm yields comparable runtime results.