21 citations · 47 across the 8 of their papers we have counts for
12 papers
Toland duality and particle approximations for signed Wasserstein barycenters
Thomas Gallouët, Andrea Natale, Gabriele Todeschi
We study the problem of minimizing a weighted sum of squared Wasserstein distances with signed coefficients. In the case of a single positive coefficient, we derive two convex dual…
From geodesic extrapolation to a variational BDF2 scheme for Wasserstein gradient flows
Thomas Gallouët, Andrea Natale, Gabriele Todeschi
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…
Convergence of a Lagrangian discretization for barotropic fluids and porous media flow
Thomas Gallouët, Quentin Merigot, Andrea Natale
When expressed in Lagrangian variables, the equations of motion for compressible (barotropic) fluids have the structure of a classical Hamiltonian system in which the potential ene…
Simulation of multiphase porous media flows with minimizing movement and finite volume schemes
Clément Cancès, Thomas O. Gallouët, Maxime Laborde +1
The Wasserstein gradient flow structure of the PDE system governing multiphase flows in porous media was recently highlighted in [C. Cancès, T. O. Gallouët, and L. Monsaingeon, {\i…
Second order models for optimal transport and cubic splines on the Wasserstein space
Jean-David Benamou, Thomas Gallouët, François-Xavier Vialard
On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After presenting the natura…
An unbalanced Optimal Transport splitting scheme for general advection-reaction-diffusion problems
Thomas Gallouët, Maxime Laborde, Léonard Monsaingeon
In this paper, we show that unbalanced optimal transport provides a convenient framework to handle reaction and diffusion processes in a unified metric framework. We use a construc…
The Camassa-Holm equation as an incompressible Euler equation: a geometric point of view
Thomas Gallouët, François-Xavier Vialard
The group of diffeomorphisms of a compact manifold endowed with the L^2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler…
Incompressible immiscible multiphase flows in porous media: a variational approach
Clément Cancès, Thomas Gallouët, Leonard Monsaingeon
We describe the competitive motion of (N + 1) incompressible immiscible phases within a porous medium as the gradient flow of a singular energy in the space of non-negative measure…
A Lagrangian scheme for the incompressible Euler equation using optimal transport
Thomas Gallouët, Quentin Mérigot
We approximate the regular solutions of the incompressible Euler equation by the solution of ODEs on finite-dimensional spaces. Our approach combines Arnold's interpretation of the…
A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows
Thomas Gallouët, Léonard Monsaingeon
In this article we set up a splitting variant of the JKO scheme in order to handle gradient flows with respect to the Kantorovich-Fisher-Rao metric, recently introduced and defined…
On the convexity of injectivity domains on nonfocal manifolds
Alessio Figalli, Thomas Gallouët, Ludovic Rifford
Given a smooth nonfocal compact Riemannian manifold, we show that the so-called Ma--Trudinger--Wang condition implies the convexity of injectivity domains. This improves a previous…
Particle approximation of the one dimensional Keller-Segel equation, stability and rigidity of the blow-up
Vincent Calvez, Thomas Gallouët
We investigate a particle system which is a discrete and deterministic approximation of the one-dimensional Keller-Segel equation with a logarithmic potential. The particle system…