On fast computation of finite-time coherent sets using radial basis functions

TL;DR

This paper introduces a radial basis function collocation method that significantly speeds up the computation of finite-time coherent sets by reducing the number of Lagrangian trajectories needed, making transfer operator analysis more efficient.

Contribution

It presents a novel numerical approach using radial basis functions for transfer operator construction, improving computational efficiency for advective dynamics.

Findings

Substantial speedup in transfer operator analysis.

Reduced number of Lagrangian trajectories required.

Effective detection of finite-time coherent sets.

Abstract

Finite-time coherent sets inhibit mixing over finite times. The most expensive part of the transfer operator approach to detecting coherent sets is the construction of the operator itself. We present a numerical method based on radial basis function collocation and apply it to a recent transfer operator construction that has been designed specifically for purely advective dynamics. The construction is based on a "dynamic" Laplacian operator and minimises the boundary size of the coherent sets relative to their volume. The main advantage of our new approach is a substantial reduction in the number of Lagrangian trajectories that need to be computed, leading to large speedups in the transfer operator analysis when this computation is costly.