Section: New Results
JKO gradient flow numerics
-
Benamou, Carlier, Merigot (Univ. of Grenoble, CNRS) , Oudet (Univ. of Grenoble)q
A large class of non-linear continuity equations with confinement and/or possibly non local interaction potential can be considered as semi discrete gradient flows with respect to the Euclidean Wassertein distance. The numerical resolution of such problem in dimension 2 and higher is open. Our approach is based on two remarks : the reformulation of the optimization problem in terms of Brenier potential seems to behave better. This introduces a Monge-Ampère operator in the cost functional which needs a monotone discretization in order to preserve the convexity at the discrete level. The first numerical results are very encouraging.
-
Benamou, Carlier, Agueh (Univ. of Victoria) Splitting methods for kinetic equations, we try to use one JKO step to deal with the non-linear velocity advection part of kinetic equations [31] . This seems to be relevant to granular media equation [16] , and also may offer a completely new method for Liouville equations arising from Geometrical Optics [19] .