Gradient enhanced ADMM Algorithm for dynamic optimal transport on surfaces

TL;DR

This paper introduces a gradient enhanced ADMM algorithm for dynamic optimal transport on surfaces, improving accuracy and robustness by integrating gradient recovery techniques and avoiding stagger grids.

Contribution

It presents a novel method combining gradient recovery with ADMM for optimal transport on surfaces, enhancing accuracy and robustness over existing techniques.

Findings

Improved computational accuracy for optimal transport on surfaces.

Avoids the use of stagger grids, simplifying implementation.

Demonstrates better robustness compared to other averaging methods.

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.