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dc.contributor.advisorTempone, Raul
dc.contributor.authorHaji Ali, Abdul Lateef
dc.date.accessioned2012-11-05T09:09:48Z
dc.date.available2012-11-05T09:09:48Z
dc.date.issued2012-11
dc.identifier.citationHaji Ali, A. L. (2012). Pedestrian Flow in the Mean Field Limit. KAUST Research Repository. https://doi.org/10.25781/KAUST-N103E
dc.identifier.doi10.25781/KAUST-N103E
dc.identifier.urihttp://hdl.handle.net/10754/250912
dc.description.abstractWe 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.
dc.language.isoen
dc.subjectCrowd modeling
dc.subjectMean-Field
dc.subjectHelbing
dc.subjectPedestrian
dc.subjectParticle MLMC
dc.titlePedestrian Flow in the Mean Field Limit
dc.typeThesis
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberKasimov, Aslan R.
dc.contributor.committeememberKetcheson, David I.
dc.contributor.committeememberKeyes, David E.
thesis.degree.disciplineApplied Mathematics and Computational Science
thesis.degree.nameMaster of Science


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