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

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construction [G. Froyland, Dynamic isoperimetry and the geometry of Lagrangian coherent structures, Nonlinearity (unpublished); preprint arXiv:1411.7186] that has been designed specifically for purely advective dynamics. The construction [G. Froyland, Dynamic isoperimetry and the geometry of Lagrangian coherent structures,Nonlinearity (unpublished); preprint arXiv: 1411.7186] is based on a dynamic Laplace operator and minimises the boundary size of the coherent sets relative to their volume.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. (C) 2015 AIP Publishing LLC.