A linear finite-difference scheme for approximating Randers distances on Cartesian grids
In: ISSN: 1292-8119 ; EISSN: 1262-3377, 2022
Online
academicJournal
Zugriff:
International audience ; Randers distances are an asymmetric generalization of Riemannian distances, and arise in optimal control problems subject to a drift term, among other applications. We show that Randers eikonal equation can be approximated by a logarithmic transformation of an anisotropic second order linear equation, generalizing Varadhan's formula for Riemannian manifolds. Based on this observation, we establish the convergence of a numerical method for computing Randers distances, from point sources or from a domain's boundary, on Cartesian grids of dimension two and three, which is consistent at order two thirds, and uses tools from low-dimensional algorithmic geometry for best efficiency. We also propose a numerical method for optimal transport problems whose cost is a Randers distance, exploiting the linear structure of our discretization and generalizing previous works in the Riemannian case. Numerical experiments illustrate our results.
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A linear finite-difference scheme for approximating Randers distances on Cartesian grids
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Autor/in / Beteiligte Person: | Bonnans, Frédéric ; Bonnet, Guillaume ; Mirebeau, Jean-Marie ; Dynamical Interconnected Systems in COmplex Environments (DISCO) ; Inria Saclay - Ile de France ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des signaux et systèmes (L2S) ; CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) ; Laboratoire de Mathématiques d'Orsay (LMO) ; Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) ; CB - Centre Borelli - UMR 9010 (CB) ; Service de Santé des Armées-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay)-Université Paris Cité (UPCité) ; Centre National de la Recherche Scientifique (CNRS) ; The first author was partially supported by the FiME Lab Research Initiative (Institut Europlace de Finance). |
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Zeitschrift: | ISSN: 1292-8119 ; EISSN: 1262-3377, 2022 |
Veröffentlichung: | HAL CCSD ; EDP Sciences, 2022 |
Medientyp: | academicJournal |
DOI: | 10.1051/cocv/2022043 |
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