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From geodesic extrapolation to a variational BDF2 scheme for Wasserstein gradient flows

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  • معلومة اضافية
    • Contributors:
      Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN); CEntre de REcherches en MAthématiques de la DEcision (CEREMADE); Université Paris Dauphine-PSL; Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL; Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria); Reliable numerical approximations of dissipative systems (RAPSODI ); Laboratoire Paul Painlevé (LPP); Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe; Institut des Sciences de la Terre (ISTerre); Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement IRD : UR219-Université Savoie Mont Blanc (USMB Université de Savoie Université de Chambéry )-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel-Université Grenoble Alpes (UGA); TOG acknowledges the support of the french Agence Nationale de la Recherche through the project MAGA (ANR-16-CE40-0014). GT acknowledges that this project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 754362. This work was supported in part by the Labex CEMPI (ANR-11-LABX-0007-01).; ANR-16-CE40-0014,MAGA,Monge-Ampère et Géométrie Algorithmique(2016); ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011)
    • بيانات النشر:
      HAL CCSD
    • الموضوع:
      2023
    • Collection:
      Université Grenoble Alpes: HAL
    • نبذة مختصرة :
      We introduce a time discretization for Wasserstein gradient flows based on the classical Backward Differentiation Formula of order two. The main building block of the scheme is the notion of geodesic extrapolation in the Wasserstein space, which in general is not uniquely defined. We propose several possible definitions for such an operation, and we prove convergence of the resulting scheme to the limit PDE, in the case of the Fokker-Planck equation. For a specific choice of extrapolation we also prove a more general result, that is convergence towards EVI flows. Finally, we propose a variational finite volume discretization of the scheme which numerically achieves second order accuracy in both space and time.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/2209.14622; hal-03790981; https://hal.science/hal-03790981; https://hal.science/hal-03790981v2/document; https://hal.science/hal-03790981v2/file/WassersteinExtrapolationBDF2.pdf; ARXIV: 2209.14622
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.61441586