10.5281/zenodo.5559175
https://zenodo.org/records/5559175
oai:zenodo.org:5559175
An, Dongsheng
Dongsheng
An
Stony Brook University
Lei, Na
Na
Lei
Dalian University of Technology
Zhao, Tong
Tong
Zhao
Université Côte d'Azur
Si, Hang
Hang
Si
Weierstrass Institute for Applied Analysis and Stochastics
Gu, Xianfeng
Xianfeng
Gu
Stony Brook University
A Moving Mesh Adaptation Method by Optimal Transport
Zenodo
2021
Optimal transport
Monge-Ampère equation
Adaptive mesh
2021-10-09
eng
10.5281/zenodo.5559174
https://zenodo.org/communities/imr29
Creative Commons Attribution 4.0 International
Optimal transportation finds the most economical way to transport one probability measure to another, and it plays an important role in geometric modeling and processing. In this paper, we propose a moving mesh method to generate adaptive meshes by optimal transport. Given an initial mesh and a scalar density function defined on the mesh domain, our method will redistribute the mesh nodes such that they are adapted to the density function. Based on the Brenier theorem, solving an optimal transportation problem is reduced to solving a Monge-Ampère equation, which is difficult to compute due to the high non-linearity. On the other hand, the optimal transportation problem is equivalent to the Alexandrov problem, which can finally induce an effective variational algorithm. Experiments show that our proposed method finds the adaptive mesh quickly and efficiently.