Computing the finite time Lyapunov exponent for flows with uncertainties
数学专题报告
报告题目(Title)：Computing the finite time Lyapunov exponent for flows with uncertainties
报告人(Speaker)：尤国桥 （南京审计大学副教授)
地点(Place)：腾讯会议号 685-852-083
时间(Time)：2022 年 6 月 7日（周二） 18:00--19:00
邀请人(Inviter)：刘 君
报告摘要
We propose an Eulerian approach to compute the expected finite time Lyapunov exponent (FTLE) of uncertain flow fields. The definition extends the usual FTLE for deterministic dynamical systems. Instead of performing Monte Carlo simulations as in typical Lagrangian computations, our approach associates each initial flow particle with a probability density function (PDF) which satisfies an advection-diffusion equation known as the Fokker-Planck (FP) equation. Numerically, we incorporate Strang’s splitting scheme so that we can obtain a second-order accurate solution to the equation. To further improve the computational efficiency, we develop an adaptive approach to concentrate the computation of the FTLE near the ridge, where the so-called Lagrangian coherent structure (LCS) might exist. We will apply our proposed algorithm to several test examples including a real-life dataset to demonstrate the performance of the method.
主讲人简介
尤国桥，南京审计大学副教授，应用数学系主任，入选江苏省“青蓝工程”优秀青年骨干教师、江苏省“双创博士”。主要研究方向为非线性动力系统可视化、数值计算。主要研究结果发表在SIAM J. Sci. Comput., J. Comput. Phys., J. Sci. Comput.等计算数学领域国际知名期刊上。主持参与多项国家自然科学基金项目。
