Numerical solution of the Optimal Transportation problem using the Monge–Ampère equation

Abstract : A numerical method for the solution of the elliptic Monge–Ampère Partial Differential Equation, with boundary conditions corresponding to the Optimal Transportation (OT) problem, is presented. A local representation of the OT boundary conditions is combined with a finite difference scheme for the Monge–Ampère equation. Newtonʼs method is implemented, leading to a fast solver, comparable to solving the Laplace equation on the same grid several times. Theoretical justification for the method is given by a convergence proof in the companion paper [4]. Solutions are computed with densities supported on non-convex and disconnected domains. Computational examples demonstrate robust performance on singular solutions and fast computational times
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Journal of Computational Physics, Elsevier, 2014, 260 (1), pp.107-126. 〈10.1016/j.jcp.2013.12.015〉
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https://hal.inria.fr/hal-01115626
Contributeur : Brigitte Briot <>
Soumis le : mercredi 11 février 2015 - 14:07:00
Dernière modification le : vendredi 25 mai 2018 - 12:02:06

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Jean-David Benamou, Brittany D. Froese, Adam M. Oberman. Numerical solution of the Optimal Transportation problem using the Monge–Ampère equation. Journal of Computational Physics, Elsevier, 2014, 260 (1), pp.107-126. 〈10.1016/j.jcp.2013.12.015〉. 〈hal-01115626〉

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