PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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
Abstract:
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

Room Number:MB106
Date:04 / 19 / 2011
Time:04:00pm - 05:00pm