• Refine Query
  • Source
  • Publication year
  • to
  • Language
  • 2
  • Tagged with
  • 2
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1
  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Pedestrian Flow in the Mean Field Limit

Haji Ali, Abdul Lateef 11 1900 (has links)
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.
2

A Full Multigrid-Multilevel Quasi-Monte Carlo Approach for Elliptic PDE with Random Coefficients

Liu, Yang 05 May 2019 (has links)
The subsurface flow is usually subject to uncertain porous media structures. However, in most cases we only have partial knowledge about the porous media properties. A common approach is to model the uncertain parameters as random fields, then the expectation of Quantity of Interest(QoI) can be evaluated by the Monte Carlo method. In this study, we develop a full multigrid-multilevel Monte Carlo (FMG-MLMC) method to speed up the evaluation of random parameters effects on single-phase porous flows. In general, MLMC method applies a series of discretization with increasing resolution and computes the QoI on each of them, the success of which lies in the effective variance reduction. We exploit the similar hierarchies of MLMC and multigrid methods, and obtain the solution on coarse mesh Qcl as a byproduct of the multigrid solution on fine mesh Qfl on each level l. In the cases considered in this thesis, the computational saving is 20% theoretically. In addition, a comparison of Monte Carlo and Quasi-Monte Carlo (QMC) methods reveals a smaller estimator variance and faster convergence rate of the latter method in this study.

Page generated in 0.0224 seconds