We study the meanfield limit of a particlebased 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 meanfield limit, the timedependent density of twodimensional pedestrians satisfies a fourdimensional integrodifferential FokkerPlanck equation. To approximate the solution of the FokkerPlanck equation we use a timesplitting approach and solve the diffusion part using a CrankNicholson method. The advection part is solved using a LaxWendroffLeveque method or an upwind Backward Euler method depending on the advection speed.
Moreover, we use multilevel Monte Carlo to estimate observables from the particlebased system. We discuss these numerical methods, and present numerical results showing the convergence of observables that were calculated using the particlebased model as the number of pedestrians increases to those calculated using the probability density function satisfying the FokkerPlanck equation.
Date of Award  Nov 2012 

Original language  English (US) 

Awarding Institution   Computer, Electrical and Mathematical Science and Engineering


Supervisor  Raul Tempone (Supervisor) 

 Crowd modeling
 MeanField
 Helbing
 Pedestrian
 Particle MLMC