针对一般非线性迁移率的Wasserstein类梯度流的高效原始-对偶前向后向分割方法

我们构造了一种高效的原始-对偶前向后向 (PDFB) 分割方法，用于计算具有非线性迁移率传输距离的最小移动方案的一类问题，并将其用于计算Wasserstein类梯度流。该方法引入了一种新的鞍点形式，用于最小移动方案，利用来自Benamou-Brenier动态最优传输公式的支撑函数形式。 resulting framework allows for flexible computation of Wasserstein-like gradient flows by solving the corresponding saddle point problem at the fully discrete level, and can be easily extended to handle general nonlinear mobilities. We also provide a detailed convergence analysis of the PDFB splitting method, along with practical remarks on its implementation and application. The effectiveness of the method is demonstrated through several challenging numerical examples.