Minimal geodesics along volume preserving maps, through semi-discrete optimal transport

Abstract : We introduce a numerical method for extracting minimal geodesics along the group of volume preserving maps, equipped with the L 2 metric, which as observed by Arnold [Arn66] solve Euler's equations of inviscid incompressible fluids. The method relies on the generalized polar decomposition of Brenier [Bre91], numerically implemented through semi-discrete optimal transport. It is robust enough to extract non-classical, multi-valued solutions of Eu-ler's equations, for which the flow dimension is higher than the domain dimension, a striking and unavoidable consequence of this model [Shn94]. Our convergence results encompass this generalized model, and our numerical experiments illustrate it for the first time in two space dimensions.
Type de document :
Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01152168
Contributeur : Quentin Mérigot <>
Soumis le : vendredi 15 mai 2015 - 13:21:29
Dernière modification le : vendredi 16 décembre 2016 - 01:05:02
Document(s) archivé(s) le : jeudi 20 avril 2017 - 00:12:02

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EulerConvergence.pdf
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  • HAL Id : hal-01152168, version 1
  • ARXIV : 1505.03306

Citation

Quentin Mérigot, Jean-Marie Mirebeau. Minimal geodesics along volume preserving maps, through semi-discrete optimal transport. 2015. 〈hal-01152168v1〉

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