Structure preserving schemes for a class of Wasserstein gradient flows

TL;DR

This paper presents two novel time discretization schemes for Wasserstein gradient flows that preserve key properties like mass, positivity, and energy dissipation, validated through extensive numerical experiments.

Contribution

Introduction of two new discretization schemes for Wasserstein gradient flows that maintain physical properties and improve numerical robustness.

Findings

Schemes preserve mass, positivity, and energy dissipation.

Numerical experiments confirm robustness and accuracy.

Schemes are computationally efficient.

Abstract

We introduce in this paper two time discretization schemes tailored for a range of Wasserstein gradient flows. These schemes are designed to preserve mass, positivity and to be uniquely solvable. In addition, they also ensure energy dissipation in many typical scenarios. Through extensive numerical experiments, we demonstrate the schemes' robustness, accuracy and efficiency.