Title: Multiscale Methods for Increased Tractability in Stochastic Collocation for Flow in Porous Media

Speaker: Professor Benjamin Ganis, University of Pittsburgh

Date/Time: Wednesday, December 2, 2009, 10:00 – 11:00 am        

Location: CSRI Building, Room 95 (Sandia NM)

Brief Abstract: In this talk I will present an efficient multiscale stochastic framework for uncertainty quantification of flow through porous media.  The governing equations are based on Darcy's law with nonstationary stochastic permeability represented as a sum of Karhunen-Loeve expansions, meant to represent multiple rock types.  The approximation uses stochastic collocation on either a tensor product or a sparse grid, and couples it with a domain decomposition algorithm known as the Multiscale Mortar Mixed Finite Element Method.  The traditional implementation of this method formulates a coarse scale mortar interface problem, and solves it with an iterative method that requires the solution of local fine scale linear systems on each iteration.  A modification of this method called the Multiscale Flux Basis Implementation has recently been developed, which reuses the solutions of these linear systems during the iteration.  This idea is extended into the stochastic setting to formulate collocation algorithms that are more efficient than the traditional implementation by orders of magnitude.  Error analysis and numerical experiments will be presented.

CSRI POC: James Stewart, (505) 844-8630