EAS PHD Prosposal Defense by Christopher L. Bresten
When: Tuesday,
December 6, 2016
9:20 AM
-
11:20 AM
Where: Textiles Building 105
Description: TITLE: ON THE REDUCED COLLOCATION METHOD FOR NON-LINEAR STEADY-STATE PDEs AND PEDESTRIAN TRAFFIC FLOWS
abstract: Reduced basis methods are a class of numerical methods developed for settings which require a large number of solutions to a parameterized problem. In this work, we consider settings which require many queries to a numerical solver for a parameterized steady-state partial differential equation. We adapt an existing method for linear steady-state problems, the reduced collocation method, to the non-linear case.
Furthermore, a class of 2-D non-linear hyperbolic PDEs for pedestrian traffic flow is considered. An appropriate numerical solver is furnished using weighted essentially non-oscillatory finite difference in space, and a strong stability preserving Runge-Kutta method in time. Several models in this class are approached, one extended with a novel non-local path-planning formulation.
Some of these models have physical parameters that are difficult to measure directly. This yields a parameter estimation problem on the steady-state solution. The resulting PDE constrained optimal control problem, requiring many queries to the solver, is accelerated with the reduced collocation method.
abstract: Reduced basis methods are a class of numerical methods developed for settings which require a large number of solutions to a parameterized problem. In this work, we consider settings which require many queries to a numerical solver for a parameterized steady-state partial differential equation. We adapt an existing method for linear steady-state problems, the reduced collocation method, to the non-linear case.
Furthermore, a class of 2-D non-linear hyperbolic PDEs for pedestrian traffic flow is considered. An appropriate numerical solver is furnished using weighted essentially non-oscillatory finite difference in space, and a strong stability preserving Runge-Kutta method in time. Several models in this class are approached, one extended with a novel non-local path-planning formulation.
Some of these models have physical parameters that are difficult to measure directly. This yields a parameter estimation problem on the steady-state solution. The resulting PDE constrained optimal control problem, requiring many queries to the solver, is accelerated with the reduced collocation method.
Contact: EAS Seminar Series
Topical Areas: University Community, MBA or Graduate, Mathematics, College of Engineering