Title: Efficient Uncertainty Quantification and a posteriori Error Estimation for Multiscale Mortar Method Speaker: Timothy Wildey, The University of Texas at Austin Date/Time: Wednesday, September 8, 2010 at 10:00 – 11:00am Location: CSRI Building/Room 90 (Sandia NM) Brief Abstract: Mortar domain decomposition methods have become popular in recent years due to their ability to handle nonmatching interface grids as well as multiphysics and multinumerics coupling. Recent work has shown that the mortar methods can also be interpreted as multiscale methods whereby the construction of a multiscale mortar basis may be beneficial in solving the coarse scale interface problem. An important question is whether this multiscale interpretation is amenable or advantageous for uncertainty quantification and/or a posteriori error estimation. In the first part of this talk, we consider stochastic collocation methods for uncertainty quantification of single and two phase flow with a stochastic permeability field. We then show that the multiscale interpretation leads a multiscale preconditioner which greatly reduces the overall computational cost in computing the desired statistical quantities. Next, we consider discretization of a deterministic elliptic problem by means of different numerical methods applied separately in different subdomains of the computational domain and coupled using the mortar technique. We derive several fully computable a posteriori error estimates which deliver a guaranteed upper bound on the error measured in the energy norm. Our estimates are also locally efficient and one of them is robust with respect to the ratio of scales under an assumption of sufficient regularity. This approach allows us to bound separately and to compare mutually the subdomain and interface errors. If time permits, we will also discuss a combination of uncertainty quantification and adjoint-based a posteriori error estimation where a polynomial chaos representation of the adjoint solution is used to cheaply produce error estimates for a linear functional of the forward solution without repeated forward/adjoint solves.CSRI POC: James R. Stewart, 505-844-8630 |