Structure preserving schemes for a class of Wasserstein gradient flows

2024/07/12 by Shiheng Zhang, Jie Shen, Zhang, Shiheng +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #35K55 #35K61 #65M12 #65Z05 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Heme Oxygenase-1 and Carbon Monoxide #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2407.09416

openalex publication_date 2024/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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