Structure Preserving Schemes for a Class of Wasserstein Gradient Flows

doi:10.1007/s42967-025-00486-2

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (3): 1174-1194.doi: 10.1007/s42967-025-00486-2

• ORIGINAL PAPERS • 上一篇

Structure Preserving Schemes for a Class of Wasserstein Gradient Flows

Shiheng Zhang¹, Jie Shen²

1 Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA;
2 School of Mathematical Science, Eastern Institute of Technology, Ningbo 315200, Zhejiang, China

收稿日期:2024-03-27 修回日期:2024-08-28 接受日期:2024-10-14 出版日期:2025-09-20 发布日期:2025-05-23
通讯作者: Jie Shen, jshen@eitech.edu.cn;Shiheng Zhang, shzhang3@uw.edu E-mail:jshen@eitech.edu.cn;shzhang3@uw.edu
基金资助:
This work was partially supported by the NSFC (Grant No. 12371409).

Structure Preserving Schemes for a Class of Wasserstein Gradient Flows

Shiheng Zhang¹, Jie Shen²

1 Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA;
2 School of Mathematical Science, Eastern Institute of Technology, Ningbo 315200, Zhejiang, China

Received:2024-03-27 Revised:2024-08-28 Accepted:2024-10-14 Online:2025-09-20 Published:2025-05-23
Supported by:
This work was partially supported by the NSFC (Grant No. 12371409).

摘要/Abstract

摘要： We introduce in this paper two time discretization schemes tailored for a range of Wasserstein gradient flows. These schemes are designed to preserve mass and 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.

关键词: Wasserstein gradient flow, Positivity preserving, Energy stability, Porous media equation (PME)

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 and 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.

Key words: Wasserstein gradient flow, Positivity preserving, Energy stability, Porous media equation (PME)

中图分类号:

Shiheng Zhang, Jie Shen. Structure Preserving Schemes for a Class of Wasserstein Gradient Flows[J]. Communications on Applied Mathematics and Computation, 2025, 7(3): 1174-1194.

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Structure Preserving Schemes for a Class of Wasserstein Gradient Flows

Structure Preserving Schemes for a Class of Wasserstein Gradient Flows

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