论文标题
Lagrangian的Lagrangian方案用于Wasserstein梯度流
Lagrangian schemes for Wasserstein gradient flows
论文作者
论文摘要
本文回顾了Wasserstein梯度流的特定示例的不同数值方法：我们专注于非线性fokker-Planck方程，但也讨论了抛物线纤维纤维性Keller-segel模型和第四阶薄膜方程的离散化。所综述的方法是拉格朗日性质，即数值近似值追踪基础传输方程的特征，而不是直接求解质量密度的演化方程。这两种主要方法是基于一方面集成拉格朗日图的方程，另一方面是基于单个质量颗粒的耦合odes解决方案。
This paper reviews different numerical methods for specific examples of Wasserstein gradient flows: we focus on nonlinear Fokker-Planck equations,but also discuss discretizations of the parabolic-elliptic Keller-Segel model and of the fourth order thin film equation. The methods under review are of Lagrangian nature, that is, the numerical approximations trace the characteristics of the underlying transport equation rather than solving the evolution equation for the mass density directly. The two main approaches are based on integrating the equation for the Lagrangian maps on the one hand, and on solution of coupled ODEs for individual mass particles on the other hand.
