Computation of optimal transport with finite volumes
Natale, Andrea; Todeschi, Gabriele (2021), Computation of optimal transport with finite volumes, ESAIM: Mathematical Modelling and Numerical Analysis, 55, 5, p. 1847-1871. 10.1051/m2an/2021041
TypeArticle accepté pour publication ou publié
Journal nameESAIM: Mathematical Modelling and Numerical Analysis
MetadataShow full item record
Reliable numerical approximations of dissipative systems [RAPSODI ]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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 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.
Subjects / KeywordsFinite volumes; Dynamical optimal transport; Barrier method
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