A gradient enhanced ADMM algorithm for optimal transport on general surfaces is proposed in this paper. Based on Benamou and Brenier's dynamical formulation, we combine gradient recovery techniques on surfaces with the ADMM algorithm, not only improving the computational accuracy, but also providing a novel method to deal with dual variables in the algorithm. This method avoids the use of stagger grids, has better accuracy and is more robust comparing to other averaging techniques.

翻译：本文提出了一种适用于一般曲面的梯度增强交替方向乘子法（ADMM）最优传输算法。基于Benamou与Brenier的动态表述框架，我们将曲面上的梯度恢复技术与ADMM算法相结合，不仅提升了计算精度，同时为算法中对偶变量的处理提供了一种新颖方法。相较于其他平均化技术，该方法避免了交错网格的使用，具有更高的精度与更强的鲁棒性。