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. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/3977 |
| Date | 29 August 2008 |
| Creators | Rath, James Michael, 1975- |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | electronic |
| Rights | Copyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works. |
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