Wednesday, 20 November, 2013
SPEAKER: Prof. Harbir Antil, George Mason University
TITLE: "Convergence Of Reduced Basis Methods Abstract"
ABSTRACT: When reduced basis (RB) or another projection based technique is used to generate reduced order models, the number of equations and unknowns is typically reduced dramatically. However, for nonlinear or parametrically varying problems, the cost of evaluating the reduced order models still depends on the size of the full order model and is still expensive.
We demonstrate how a combination of RB and empirical interpolation method leads to reduced order models that typically can be evaluated at a cost that only depends on the size of the reduced order model. We will apply the idea to a nonlinear parameter dependent advection diffusion equation discretized using finite element method and finally present another application for a shape optimization problem.
Recently it was shown that the RB error is related to the so-called Kolmogorov n-width of a set and if the n-width decays exponentially or algebraically so will the RB error. Therefore we will compute the n-width of a set of Banach space valued analytic functions defined on a closed bounded interval and give sufficient conditions for n-width to decay exponentially or algebraically and consequently RB error.
CAM seminar schedule: http://www.math.utk.edu/~vasili/FTP/AM/CAMseminar.html