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5 papers
Computation of Optimal Transport with Finite Volumes
Andrea Natale, Gabriele Todeschi
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 introduce…
TPFA Finite Volume Approximation of Wasserstein Gradient Flows
Andrea Natale, Gabriele Todeschi
Numerous infinite dimensional dynamical systems arising in different fields have been shown to exhibit a gradient flow structure in the Wasserstein space. We construct Two Point Fl…
Metric completion of with the right-invariant metric
Simone Di Marino, Andrea Natale, Rabah Tahraoui +1
We consider the group of smooth increasing diffeomorphisms Diff on the unit interval endowed with the right-invariant metric. We compute the metric completion of this space w…
Generalized compressible flows and solutions of the H(div) geodesic problem
Thomas Gallouët, Andrea Natale, François-Xavier Vialard
We study the geodesic problem on the group of diffeomorphism of a domain MRd, equipped with the H(div) metric. The geodesic equations coincide with the Camassa-Holm equati…
Embedding Camassa-Holm equations in incompressible Euler
François-Xavier Vialard, Andrea Natale
In this article, we show how to embed the so-called CH2 equations into the geodesic flow of the Hdiv metric in 2D, which, itself, can be embedded in the incompressible Euler equati…