Multi-scale parameter estimation for the steady state diffusion equation /
Parameter estimation problems where the unknown quantities
| Main Author: | |
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| Format: | Thesis Book |
| Language: | English |
| Published: |
[Place of publication not identified] :
[publisher not identified] ;
1997.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=736584771&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Parameter estimation problems where the unknown quantities have both discontinuous and spatially heterogeneous behavior on multiple length scales are very challenging, mathematically and computationally. For example, in flow through layered (or fractured) porous media, both porosity and absolute permeability will have spatial variability (and discontinuties) at multiple length scales. One can model this by representing the porosity and absolute permeability by a set of basis functions which incorporate scale dependence. One example of such a basis are the Daubechies wavelets of order N. The simplest such basis (Harr) is used for recovering discontinuous coefficients. By comparing the output of the numerical simulation and experimental data from the physical system itself, constraints on the unknowns results. When the unknowns are present at several length scales, standard least squares methods converge slowly, if at all. By representing coefficients hierarchically, and distributing the degree of freedom in an intelligent fashion, the least squares method become much more robust. A complete convergence analysis and error estimation are given. Extensive numerical experiments are implemented. The numerical results validate the convergence analysis. |
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| Item Description: | Vita. "Major Subject: Mathematics". |
| Physical Description: | viii, 101 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 89-96. |