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    Pedestrian Flow in the Mean Field Limit

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    AbdulLateef Haji Ali _Thesis.pdf
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    Type
    Thesis
    Authors
    Haji Ali, Abdul Lateef cc
    Advisors
    Tempone, Raul cc
    Committee members
    Kasimov, Aslan R. cc
    Ketcheson, David I. cc
    Keyes, David E. cc
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2012-11
    Permanent link to this record
    http://hdl.handle.net/10754/250912
    
    Metadata
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    Abstract
    We study the mean-field limit of a particle-based system modeling the behavior of many indistinguishable pedestrians as their number increases. The base model is a modified version of Helbing's social force model. In the mean-field limit, the time-dependent density of two-dimensional pedestrians satisfies a four-dimensional integro-differential Fokker-Planck equation. To approximate the solution of the Fokker-Planck equation we use a time-splitting approach and solve the diffusion part using a Crank-Nicholson method. The advection part is solved using a Lax-Wendroff-Leveque method or an upwind Backward Euler method depending on the advection speed. Moreover, we use multilevel Monte Carlo to estimate observables from the particle-based system. We discuss these numerical methods, and present numerical results showing the convergence of observables that were calculated using the particle-based model as the number of pedestrians increases to those calculated using the probability density function satisfying the Fokker-Planck equation.
    Citation
    Haji Ali, A. L. (2012). Pedestrian Flow in the Mean Field Limit. KAUST Research Repository. https://doi.org/10.25781/KAUST-N103E
    DOI
    10.25781/KAUST-N103E
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-N103E
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; MS Theses; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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