Gradient enhanced ADMM Algorithm for dynamic optimal transport on surfaces

Abstract: 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.