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Title: A Moving Mesh Adaption Method By Optimal Transport
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-Amp\`ere 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.  more » « less
Award ID(s):
1762287
NSF-PAR ID:
10291687
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Proceedings of International Meshing Roundtable
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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