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construction [G. Froyland, "Dynamic isoperimetry and the geometry of Lagrangian coherent structures," Nonlinearity (unpublished); preprint arXiv:1411.7186] that has been designed specifically for purely advective dynamics. The construction [G. Froyland, "Dynamic isoperimetry and the geometry of Lagrangian coherent structures," Nonlinearity (unpublished); preprint arXiv:1411.7186] is based on a "dynamic" Laplace operator and minimises the boundary size of the coherent sets relative to their volume.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