Multiscale basis optimization for Darcy flow


Multiscale basis optimization for Darcy flow

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Title: Multiscale basis optimization for Darcy flow
Author: Rath, James Michael, 1975-
Abstract: Simulation of flow through a heterogeneous porous medium with fine-scale features can be computationally expensive if the flow is fully resolved. Coarsening the problem gives a faster approximation of the flow but loses some detail. We propose an algorithm that obtains the fully resolved approximation but only iterates on a sequence of coarsened problems. The sequence is chosen by optimizing the shapes of the coarse finite element basis functions. As a stand-alone method, the algorithm converges globally and monotonically with a quadratic asymptotic rate. Computational experience indicates the number of iterations needed is independent of the resolution and heterogeneity of the medium. However, an externally provided error estimate is required; the algorithm could be combined as an accelerator with another iterative algorithm. A single "inner" iteration of the other algorithm would yield an error estimate; following it with an "outer" iteration of our algorithm would give a viable method.
Department: Computational and Applied Mathematics Computational Science, Engineering, and Mathematics Program
Subject: Differential equations, Elliptic--Numerical solutions Nonlinear theories Darcy's law Algorithms
Date: 2007-05

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