Pedestrian Flow in the Mean Field Limit

Handle URI:
http://hdl.handle.net/10754/250912
Title:
Pedestrian Flow in the Mean Field Limit
Authors:
Haji Ali, Abdul Lateef ( 0000-0002-6243-0335 )
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.
Advisors:
Tempone, Raul Fidel ( 0000-0003-1967-4446 )
Committee Member:
Kasimov, Aslan; Ketcheson, David I. ( 0000-0002-1212-126X ) ; Keyes, David E. ( 0000-0002-4052-7224 )
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
Nov-2012
Type:
Thesis
Appears in Collections:
Applied Mathematics and Computational Science Program; Theses; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.advisorTempone, Raul Fidelen
dc.contributor.authorHaji Ali, Abdul Lateefen
dc.date.accessioned2012-11-05T09:09:48Z-
dc.date.available2012-11-05T09:09:48Z-
dc.date.issued2012-11en
dc.identifier.urihttp://hdl.handle.net/10754/250912en
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.en
dc.language.isoenen
dc.subjectCrowd modelingen
dc.subjectMean-Fielden
dc.subjectHelbingen
dc.subjectPedestrianen
dc.subjectParticle MLMCen
dc.titlePedestrian Flow in the Mean Field Limiten
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberKasimov, Aslanen
dc.contributor.committeememberKetcheson, David I.en
dc.contributor.committeememberKeyes, David E.en
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameMaster of Scienceen
dc.person.id113302en
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