Computing coherent sets using the Fokker-Planck equation. (English) Zbl 1369.37084
Summary: We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a discretized Fokker-Planck equation. For numerical implementation, we employ spectral collocation methods and an exponential time differentiation scheme. We experimentally compare our approach with the more classical method by Ulam that is based on discretization of the transfer operator of the unperturbed flow.
MSC:
| 37M25 | Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) |
| 37N10 | Dynamical systems in fluid mechanics, oceanography and meteorology |
| 35Q84 | Fokker-Planck equations |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 76F20 | Dynamical systems approach to turbulence |
| 37C30 | Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. |
Software:
GAIOReferences:
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