当前位置: X-MOL 学术SIAM J. Numer. Anal. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Lagrangian Discretization of Crowd Motion and Linear Diffusion
SIAM Journal on Numerical Analysis ( IF 2.9 ) Pub Date : 2020-01-01 , DOI: 10.1137/19m1274201
Hugo Leclerc , Quentin Mérigot , Filippo Santambrogio , Federico Stra

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.

中文翻译:

人群运动和线性扩散的拉格朗日离散化

我们研究了遵循梯度矢量场的人群运动模型,可能还有其他相互作用项,例如吸引力/排斥力,并且我们通过拉格朗日离散化提出了其解决方案的数值方案。所得粒子的密度约束是通过每个时间步的部分最优传输问题来强制执行的。我们证明了离散度量收敛到描述第一维人群运动的连续偏微分方程的解。在第二部分中,我们展示了如何使用类似的方法来构建线性对流扩散方程的拉格朗日离散化,解释为 Wasserstein 空间中的梯度流。我们还提供了 2D 的数值实现来证明计算的可行性。
更新日期:2020-01-01
down
wechat
bug