For more information about this meeting, contact Mark Levi, Leonid Berlyand, Alexei Novikov.
|Title:||Localization and Uncertainties in Homogenization|
|Seminar:||Applied Analysis Seminar|
|Speaker:||Houman Owhadi, Caltech|
|In the first part of this talk we show how to construct localized elliptic
cell problems for homogenization with non-separated scales, high-contrast
and arbitrary deterministic coefficients. Randomness, scale separation,
mixing or ``epsilon-sequences'' are not required because the proposed method
solely relies on the compactness of the solution space. The support of cell
problems can be localized to arbitrarily small subsets of the whole domain
and explicit approximation error estimates are obtained as a function of the
size of those subsets. In the second part this talk we consider the
situation where coefficients (corresponding to microstructure and source
terms) are random and have an imperfectly known probability distributions.
Treating those distributions as optimization variables (in an infinite
dimensional, non separable space) we obtain optimal bounds on probabilities
of deviation of solutions. Surprisingly, explicit and optimal bounds show
that, with incomplete information on the probability distribution of the
microstructure, uncertainties do not necessarily propagate across scales.
Elements of the first part are joint work with Leonid Berlyand and Lei
Zhang. Elements of the second part are joint work with C. Scovel, T.
Sullivan, M. McKerns and M. Ortiz.|
Room Reservation Information
|Date:||04 / 19 / 2011|
|Time:||04:00pm - 05:00pm|