Computation of optimal transport with ...
Type de document :
Article dans une revue scientifique: Article original
DOI :
Titre :
Computation of optimal transport with finite volumes
Auteur(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]
Titre de la revue :
ESAIM: Mathematical Modelling and Numerical Analysis
Pagination :
1847-1871
Éditeur :
Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP
Date de publication :
2021-09
ISSN :
2822-7840
Mot(s)-clé(s) en anglais :
Finite volumes
Dynamical optimal transport
Barrier method
Dynamical optimal transport
Barrier method
Discipline(s) HAL :
Mathématiques [math]
Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >
Lire la suite >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.Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
Projet ANR :
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