An improved Eulerian approach for the finite time Lyapunov exponent
type: Item
instance of: scholarly article
title: An improved Eulerian approach for the finite time Lyapunov exponent
zbMATH Open document ID: 1417.65156
author: Guoqiao You
author: Shingyu Leung
published in: Journal of Scientific Computing
publication date: 2018-09-28T00:00:00Z
review text: Proposed is a new Eulerian numerical approach to compute the Jacobian of flow maps in continuous dynamical systems and, subsequently, the so-called finite time Lyapunov exponent (FTLE) for Lagrangian coherent structure extraction. The original approach computes the flow map and then numerically determines the Jacobian of the map using finite differences. The new algorithm improves the original Eulerian formulation so that at first partial differential equations for each component of the Jacobian are obtained, and then these equations are solved to obtain the required Jacobian. For periodic dynamical systems, based on the time doubling technique developed for computing the longtime flow map, a new efficient iterative method is also proposed to compute the Jacobian of the longtime flow map. Numerical examples demonstrate that the new proposed approach is more accurate than the original one in computing the Jacobian and thus the FTLE field, especially near the FTLE ridges.
reviewed by: Ilia V. Boikov
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65P99
Mathematics Subject Classification ID: 37M25
zbMATH DE Number: 6945480
zbMATH Keywords: partial differential equations
zbMATH Keywords: flow maps
zbMATH Keywords: coherent structures
zbMATH Keywords: finite time Lyapunov exponent
zbMATH Keywords: flow visualization
describes a project that uses: VIALS
MaRDI profile type: Publication
full work available at URL: s10915-018-0669-y
OpenAlex ID: W2791673777
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DOI: 10.1007/S10915-018-0669-Y
description: scientific article; zbMATH DE number 6945480