Title: Uncertainty Quantification using Multiscale Methods and Stochastic Finite Element Methods for Porous Media Flows Speaker: Paul Dostert, Texas A&M University, Postdoctoral Candidate Date/Time: Tuesday, January 16, 2007, 9:00 am – 10:00 am Location: CSRI Building, Room 90 (Sandia NM) Brief Abstract: We develop an efficient sampling technique for dynamic data integration using Langevin algorithms. Based on a coarse-scale model of the problem, we compute the proposals of the Langevin algorithms using the coarse-scale gradient of the target distribution. Comparing with the direct Langevin algorithm, the new method generates a modified Markov chain by incorporating the coarse-scale information of the problem. We present numerical examples for sampling permeability fields. A Karhunen-Loeve expansion is used to represent the realizations of the permeability field conditioned to the dynamic data, such as the production data, as well as the static data. The numerical examples show that the coarse-gradient Langevin algorithms are much faster than the direct Langevin algorithms but have similar acceptance rates. We discuss modifications to this technique that include collocation methods and polynomial chaos approximations. |