Computation of optimal transport with ...
Document type :
Article dans une revue scientifique: Article original
DOI :
Title :
Computation of optimal transport with finite volumes
Author(s) :
Natale, Andrea [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Todeschi, Gabriele [Auteur correspondant]
Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales [MOKAPLAN]
Reliable numerical approximations of dissipative systems [RAPSODI]
Todeschi, Gabriele [Auteur correspondant]
Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales [MOKAPLAN]
Journal title :
ESAIM: Mathematical Modelling and Numerical Analysis
Pages :
1847-1871
Publisher :
Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP
Publication date :
2021-09
ISSN :
2822-7840
English keyword(s) :
Finite volumes
Dynamical optimal transport
Barrier method
Dynamical optimal transport
Barrier method
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
We construct Two-Point Flux Approximation (TPFA) finite volume schemes to solve the quadratic optimal transport problem in its dynamic form, namely the problem originally introduced by Benamou and Brenier. We show numerically ...
Show more >We construct Two-Point Flux Approximation (TPFA) finite volume schemes to solve the quadratic optimal transport problem in its dynamic form, namely the problem originally introduced by Benamou and Brenier. We show numerically that these type of discretizations are prone to form instabilities in their more natural implementation, and we propose a variation based on nested meshes in order to overcome these issues. Despite the lack of strict convexity of the problem, we also derive quantitative estimates on the convergence of the method, at least for the discrete potential and the discrete cost. Finally, we introduce a strategy based on the barrier method to solve the discrete optimization problem.Show less >
Show more >We construct Two-Point Flux Approximation (TPFA) finite volume schemes to solve the quadratic optimal transport problem in its dynamic form, namely the problem originally introduced by Benamou and Brenier. We show numerically that these type of discretizations are prone to form instabilities in their more natural implementation, and we propose a variation based on nested meshes in order to overcome these issues. Despite the lack of strict convexity of the problem, we also derive quantitative estimates on the convergence of the method, at least for the discrete potential and the discrete cost. Finally, we introduce a strategy based on the barrier method to solve the discrete optimization problem.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
ANR Project :
Collections :
Source :
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