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Fast Construction of Forward Flow Maps using Eulerian Based Interpolation Schemes

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We propose a modification to a recently developed Eulerian interpolation scheme for constructing the flow map for autonomous, periodic and aperiodic dynamical systems. We show that the proposed methods significantly… Click to show full abstract

We propose a modification to a recently developed Eulerian interpolation scheme for constructing the flow map for autonomous, periodic and aperiodic dynamical systems. We show that the proposed methods significantly improve the computational efficiency when a large number of flow maps are needed, yet retain second-order accuracy as in the original approach. The idea is to pre-compute and to store a carefully selected set of intermediate flow maps. When the initial and the final time of a required flow map are known, our proposed methods can simply load these pre-processed short-time flow maps for flow map construction. Numerical examples are included to validate our theoretical prediction, and demonstrate the effectiveness of these proposed Eulerian interpolation schemes as a simple numerical tool for other applications such as the finite-time Lyapunov exponent in determining the Lagrangian coherent structure of dynamical systems and the geometrical optics problems.

Keywords: construction; flow map; flow maps; flow; interpolation schemes

Journal Title: Journal of Scientific Computing
Year Published: 2020

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