| Abstract: |
| In 2010 we introduced, together with Maury and Roudneff-Chupin, a simple evolution model for crowd motion which happens to be a gradient flow in the Wasserstein space $W_2$ of a potential energy with a density constraint. Recently, with Hraivoronska we proposed a full discretization of some Wasserstein gradient flows on a fixed grid and found the necessary and sufficient condition in terms of the time and space steps to obtain convergence. This method is particularly efficient in the case of the crowd motion gradient flow, as it only requires to solve a sequence of linear programming problems. In a joint ongoing work with A. Gallou\et and Hraivoronska we exploit this in order to obtain efficient numerical simulations: I will present these results and all the strategies that we develop to reduce the corresponding computational cost. |
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