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- Giving to Math

Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Monday, October 6, 2008 - 05:00

Location:

Bexell 323

Guest Speaker:

Institution:

The University of Texas at Austin

Abstract:

The representer method was originally proposed for data assimilation in oceanography. The method solves the Euler-Lagrange equations arising from minimizing the data misfit subject to model constraints, by reducing the problem to the computation of "representer" functions and an expansion of the solution in terms of a forward model solution and the representers. For linear problems, the method is exact. For nonlinear problems such as those arising in parameter estimation, we propose an iterative representer based scheme, whereby the representer method is applied to the Euler-Lagrange equations arising from the minimization of the data misfit subject to the constraints imposed by the first order conditions applied to the nonlinear model. We also describe the combination of the representer method for determining geologically consistent representations of the unknown permeability, described using a Karhunen-Loeve expansion. Theoretical results for single phase flow problems will be described and numerical results for single and two phase flow will be given.