Oberseminar Numerische Mathematik / Scientific Computing
Omar Knio
Johns Hopkins University, Baltimore
Spectral Methods of Uncertainty Quantification
Abstract:
This talk outlines recent developments in spectral methods for uncertainty quantification in model-based simulations, and selected applications to problems in fluid dynamics and materials science. The fundamental principle of stochastic spectral 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 the development and implementation of robust methods that can accommodate challenging situations where the solution exhibits steep or discontinuous dependence on the random in puts. We conclude with a brief discussion of research directions that are anticipated to result in substantial benefits.
| Datum: | 31.05.10 | Zeit: | 17:00 Uhr | Ort: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Raum: | 031 im Erdgeschoss |