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Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 2020

Lagrangian discretization of crowd motion and linear diffusion

Résumé

We study a model of crowd motion following a gradient vector field, with possibly additional interaction terms such as attraction/repulsion, and we present a numerical scheme for its solution through a Lagrangian discretization. The density constraint of the resulting particles is enforced by means of a partial optimal transport problem at each time step. We prove the convergence of the discrete measures to a solution of the continuous PDE describing the crowd motion in dimension one. In a second part, we show how a similar approach can be used to construct a Lagrangian discretization of a linear advection-diffusion equation, interpreted as a gradient flow in Wasserstein space. We provide also a numerical implementation in 2D to demonstrate the feasibility of the computations.
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Dates et versions

hal-02124815 , version 1 (15-05-2019)
hal-02124815 , version 2 (28-04-2020)

Identifiants

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Hugo Leclerc, Quentin Mérigot, Filippo Santambrogio, Federico Stra. Lagrangian discretization of crowd motion and linear diffusion. SIAM Journal on Numerical Analysis, 2020, 58 (4), pp.2093-2118. ⟨10.1137/19M1274201⟩. ⟨hal-02124815v2⟩
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