使用结构保留有限体积方案对代理控制的行人动力学进行数值研究

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2023-12-28 DOI:10.1007/s10444-023-10098-0

Jan-Frederik Pietschmann, Ailyn Stötzner, Max Winkler

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引用次数: 0

摘要

我们对 Herzog 等人（Appl. Math. Optim.Optim.88(3):87, 2023).该模型由休斯行人动力学模型的正则化变体和常微分方程组成，常微分方程描述了能通过吸引力影响人群的代理人的运动。我们设计了一种有限体积方案，该方案保留了模型固有的箱体约束，并讨论了它的一些特性。我们将这一方案应用于针对疏散场景定制的目标函数。最后，我们对几种实际相关的几何形状进行了数值模拟。

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Numerical investigation of agent-controlled pedestrian dynamics using a structure-preserving finite volume scheme

We provide a numerical realization of an optimal control problem for pedestrian motion with agents that was analyzed in Herzog et al. (Appl. Math. Optim. 88(3):87, 2023). The model consists of a regularized variant of Hughes’ model for pedestrian dynamics coupled to ordinary differential equations that describe the motion of agents which are able to influence the crowd via attractive forces. We devise a finite volume scheme that preserves the box constraints that are inherent in the model and discuss some of its properties. We apply our scheme to an objective functional tailored to the case of an evacuation scenario. Finally, numerical simulations for several practically relevant geometries are performed.

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来源期刊

Advances in Computational Mathematics 数学-应用数学

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.