Year: 2019
Author: Yu-Keung Ng, Shingyu Leung
Communications in Computational Physics, Vol. 26 (2019), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0149
Communications in Computational Physics, Vol. 26 (2019), Iss. 4 : pp. 1143–1177
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Dynamical system visualization finite time Lyapunov exponent numerical methods for differential equations.