SEMINAR: Professor Omar Knio,Slab seminar room S/A 103,Tuesday,April 6,3:00 p.m.

[Sandrine Apelbaum <sapelbaum@rsmas.miami.edu>]

MPO Seminar

Professor Omar Knio

Whiting School of Engineering

Johns Hopkins University

Title:  Spectral Methods for Uncertainty Quantification

Date: Tuesday, April 6 at 3:00 p.m.

Room: Slab Seminar Room, S/A 103

Abstract:  

 This talk outlines recent developments in spectral methods for uncertainty quantification in model-based simulations, and their applications to problems in fluid dynamics.  The fundamental principle of these methods is to parametrize model uncertainty in terms of a finite set of random variables with known probability law, and to express the solution in terms of orthogonal basis functions that are typically polynomials in these random variables.  The unknown coefficients in the expansion are determined using a weighted residual formalism, which provides quantitative estimate of the dependence of the solution on random model inputs. Elementary examples will first be discussed in order to highlight fundamental concepts.  Attention will then be focused on more challenging situation where the solution exhibits steep or discontinuous dependence on the random inputs.  Under these scenarios, severe difficulties arise in the application of linearized methods, where local derivatives may not be well defined, and of spectral methods based on global polynomials bases, where Gibbs phenomena may result in decreased convergence rates or even numerical instabilities.  In contrast, it is shown that alternative spectral representations using wavelet or multiwavelet bases can provide robust and efficient means of addressing some of the associated difficulties.  We conclude with a brief discussion of possible generalizations and anticipated challenges.

 

Sandrine Apelbaum

Meteorology and Physical Oceanography 
Rosenstiel School of Marine and Atmospheric Science
University of Miami
4600 Rickenbacker Causeway
Miami, FL 33149-1098
Tel     (305) 421-4057
Fax     (305) 421-4696

sapelbaum@rsmas.miami.edu