报告题目：Structure Preserving Methods Based on Minimizing Movement Scheme for Gradient Flows with Respect to Transport Distances

报告时间：2022-12-06  15:00 - 16:30

报告人：魏朝祯 特聘研究员  电子科技大学

腾讯会议ID：345 773 4983

报告链接：https://meeting.tencent.com/p/3457734983

Abstract：In this talk, I will present a novel numerical method for gradient flows with respect to a class of transport distances induced by concentration-dependent mobilities (including the Wasserstein distance and its generalized versions), which arise widely in applications such as porous median flows, material science, and biological swarms. Based on the minimizing movement/JKO scheme, along with the dynamical characterization of the transport distances, we construct a fully discrete scheme that ends up with a minimization problem with strictly convex objective function and linear constraint, which can be solved by a recent primal dual three operator splitting scheme. Our method has built-in positivity or bounds preserving, mass conservation, and entropy decreasing properties, and overcomes stability issue due to the strong nonlinearity and degeneracy. At last, I will show some simulation results for computing Wasserstein geodesics, nonlinear Fokker-Planck equations, aggregation-diffusion equations, Cahn-Hilliard equations with degenerate mobility and wetting boundary conditions.