Volume 26, Issue 4
Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories

Yu-Keung Ng & Shingyu Leung

Commun. Comput. Phys., 26 (2019), pp. 1143-1177.

Published online: 2019-07

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  • Abstract

We propose a simple numerical algorithm to estimate the finite time Lyapunov exponent (FTLE) in dynamical systems from only a sparse number of Lagrangian particle trajectories. The method first reconstructs the flow field using the radial basis function (RBF) and then uses either the Lagrangian or the Eulerian approach to determine the corresponding flow map. We also develop a simple algorithm based on the Schur complement for updating, rather than recomputing, the reconstruction in the RBF when new trajectory data is made available in applications. We will demonstrate the effectiveness of the proposed method using examples from autonomous and aperiodic flows, and also measurements from real-life data.

  • Keywords

Dynamical system, visualization, finite time Lyapunov exponent, numerical methods for differential equations.

  • AMS Subject Headings

37M05, 37M25, 37M99, 65L05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ykngad@ust.hk (Yu-Keung Ng)

masyleung@ust.hk (Shingyu Leung)

  • BibTex
  • RIS
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@Article{CiCP-26-1143, author = {Ng , Yu-Keung and Leung , Shingyu }, title = {Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {4}, pages = {1143--1177}, abstract = {

We propose a simple numerical algorithm to estimate the finite time Lyapunov exponent (FTLE) in dynamical systems from only a sparse number of Lagrangian particle trajectories. The method first reconstructs the flow field using the radial basis function (RBF) and then uses either the Lagrangian or the Eulerian approach to determine the corresponding flow map. We also develop a simple algorithm based on the Schur complement for updating, rather than recomputing, the reconstruction in the RBF when new trajectory data is made available in applications. We will demonstrate the effectiveness of the proposed method using examples from autonomous and aperiodic flows, and also measurements from real-life data.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0149}, url = {http://global-sci.org/intro/article_detail/cicp/13232.html} }
TY - JOUR T1 - Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories AU - Ng , Yu-Keung AU - Leung , Shingyu JO - Communications in Computational Physics VL - 4 SP - 1143 EP - 1177 PY - 2019 DA - 2019/07 SN - 26 DO - http://doi.org/10.4208/cicp.OA-2018-0149 UR - https://global-sci.org/intro/article_detail/cicp/13232.html KW - Dynamical system, visualization, finite time Lyapunov exponent, numerical methods for differential equations. AB -

We propose a simple numerical algorithm to estimate the finite time Lyapunov exponent (FTLE) in dynamical systems from only a sparse number of Lagrangian particle trajectories. The method first reconstructs the flow field using the radial basis function (RBF) and then uses either the Lagrangian or the Eulerian approach to determine the corresponding flow map. We also develop a simple algorithm based on the Schur complement for updating, rather than recomputing, the reconstruction in the RBF when new trajectory data is made available in applications. We will demonstrate the effectiveness of the proposed method using examples from autonomous and aperiodic flows, and also measurements from real-life data.

Yu-Keung Ng & Shingyu Leung. (2019). Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories. Communications in Computational Physics. 26 (4). 1143-1177. doi:10.4208/cicp.OA-2018-0149
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