Parallel Algorithms for the Determination of Lyapunov Characteristics of Large Nonlinear Dynamical Systems (original) (raw)

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.

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Authors and Affiliations

1. Institute of Physics, Technical University Chemnitz, 09111, Chemnitz, Germany
   Günter Radons & Hong-liu Yang
2. Department of Computer Science, Technical University Chemnitz, 09111, Chemnitz, Germany
   Gudula Rünger & Michael Schwind

Authors

1. Günter Radons
2. Gudula Rünger
3. Michael Schwind
4. Hong-liu Yang

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Editors and Affiliations

1. Computer Science Department, University of Tennessee, 37996-3450, Knoxville, TN, USA
   Jack Dongarra
2. Department of Informatics and Mathematical Modelling, Technical University of Denmark, DK-2800, Lyngby, Denmark
   Kaj Madsen
3. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark
   Jerzy Waśniewski

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Radons, G., Rünger, G., Schwind, M., Yang, Hl. (2006). Parallel Algorithms for the Determination of Lyapunov Characteristics of Large Nonlinear Dynamical Systems. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958\_136

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• DOI: https://doi.org/10.1007/11558958\_136
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