Computational optimal transport: With applications to data science
Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
A blob method for diffusion
JA Carrillo, K Craig, FS Patacchini - Calculus of Variations and Partial …, 2019 - Springer
As a counterpoint to classical stochastic particle methods for diffusion, we develop a
deterministic particle method for linear and nonlinear diffusion. At first glance, deterministic …
deterministic particle method for linear and nonlinear diffusion. At first glance, deterministic …
Primal dual methods for Wasserstein gradient flows
Combining the classical theory of optimal transport with modern operator splitting
techniques, we develop a new numerical method for nonlinear, nonlocal partial differential …
techniques, we develop a new numerical method for nonlinear, nonlocal partial differential …
Lagrangian schemes for Wasserstein gradient flows
This chapter reviews different numerical methods for specific examples of Wasserstein
gradient flows: we focus on nonlinear Fokker-Planck equations, but also discuss …
gradient flows: we focus on nonlinear Fokker-Planck equations, but also discuss …
Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure
C Cancès, C Guichard - Foundations of Computational Mathematics, 2017 - Springer
We present a numerical method for approximating the solutions of degenerate parabolic
equations with a formal gradient flow structure. The numerical method we propose …
equations with a formal gradient flow structure. The numerical method we propose …
A variational finite volume scheme for Wasserstein gradient flows
We propose a variational finite volume scheme to approximate the solutions to Wasserstein
gradient flows. The time discretization is based on an implicit linearization of the …
gradient flows. The time discretization is based on an implicit linearization of the …
On Lagrangian schemes for porous medium type generalized diffusion equations: A discrete energetic variational approach
In this paper, we present a systematic framework to derive a variational Lagrangian scheme
for porous medium type generalized diffusion equations by employing a discrete energetic …
for porous medium type generalized diffusion equations by employing a discrete energetic …
[HTML][HTML] Boltzmann to Landau from the gradient flow perspective
We revisit the grazing collision limit connecting the Boltzmann equation to the Landau (-
Fokker–Planck) equation from their recent reinterpretations as gradient flows. Our results are …
Fokker–Planck) equation from their recent reinterpretations as gradient flows. Our results are …
Numerical study of a particle method for gradient flows
JA Carrillo, Y Huang, FS Patacchini… - arxiv preprint arxiv …, 2015 - arxiv.org
We study the numerical behaviour of a particle method for gradient flows involving linear
and nonlinear diffusion. This method relies on the discretisation of the energy via non …
and nonlinear diffusion. This method relies on the discretisation of the energy via non …
A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes
A Lagrangian numerical scheme for solving nonlinear degenerate Fokker–Planck equations
in space dimensions d ≥ 2 d≥ 2 is presented. It applies to a large class of nonlinear …
in space dimensions d ≥ 2 d≥ 2 is presented. It applies to a large class of nonlinear …