A Comparison of Nonlinear Programming Approaches to an Elliptic Inverse Problem and a New Domain Decomposition Approach (1994)
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BibTeX
@TECHREPORT{Lewis94acomparison,
author = {Robert Michael Lewis and Jr. and J. E. Dennis and Robert and Michael Lewis},
title = {A Comparison of Nonlinear Programming Approaches to an Elliptic Inverse Problem and a New Domain Decomposition Approach},
institution = {},
year = {1994}
}
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Abstract
. We compare three nonlinear programming approaches to a well-known elliptic inverse problem in three spatial dimensions. Two of these approaches may be viewed as conventional; the third approach is new and is based on a domain decomposition technique for the solution of the governing elliptic equation. We discuss the benefits that may be obtained from treating the governing differential equation in an inverse problem as equality constraints in the optimization problem. We present numerical results and discuss the relative efficacy of the three approaches. Key Words. Domain decomposition, inverse problems, large-scale nonlinear programming AMS(MOS) subject classification. Primary 90C06, secondary 49M27, 65N55, 86A05 1. Introduction We will compare three nonlinear programming approaches to a well-known elliptic inverse problem in three spatial dimensions. In the study of flow in porous media, this inverse problem is known as inverse conductivity, and involved estimating the coefficie...
