Identification of a reflection boundary coefficient in an acoustic wave equation by optimal control techniques

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The authors apply optimal control techniques to find approximate solutions to an inverse problem for the acoustic wave equation. The inverse problem (assumed here to have a solution) is to determine the boundary reflection coefficient from partial measurements of the acoustic signal. The sought reflection coefficient is treated as a control and the goal--quantified by an approximate functional--is to drive the model solution close to the experimental data by adjusting this coefficient. The problem is solved by finding the optimal control that minimizes the approximate functional. Then by driving the cost of the control to zero one proves that the ... continued below

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18 p.

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Lenhart, S.; Protopopescu, V. & Yong, J. December 31, 1997.

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This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 89 times , with 6 in the last month . More information about this article can be viewed below.

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  • Lenhart, S. Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.
  • Protopopescu, V. Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.
  • Yong, J. Fudan Univ., Shanghai (China). Dept. of Mathematics

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Description

The authors apply optimal control techniques to find approximate solutions to an inverse problem for the acoustic wave equation. The inverse problem (assumed here to have a solution) is to determine the boundary reflection coefficient from partial measurements of the acoustic signal. The sought reflection coefficient is treated as a control and the goal--quantified by an approximate functional--is to drive the model solution close to the experimental data by adjusting this coefficient. The problem is solved by finding the optimal control that minimizes the approximate functional. Then by driving the cost of the control to zero one proves that the corresponding sequence of optimal controls represents a converging sequence of estimates for the solution of the inverse problem. Compared to classical regularization methods (e.g., Tikhonov coupled with optimization schemes), their approach yields: (1) a systematic procedure to solve inverse problems of identification type and (ii) an explicit expression for the approximations of the solution.

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18 p.

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OSTI as DE99000202

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  • ISAAC `97 conference, Delaware, MD (United States), 3-7 Jun 1997

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  • Other: DE99000202
  • Report No.: ORNL/CP--99354
  • Report No.: CONF-9706289--
  • Grant Number: AC05-96OR22464
  • Office of Scientific & Technical Information Report Number: 677106
  • Archival Resource Key: ark:/67531/metadc707608

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Creation Date

  • December 31, 1997

Added to The UNT Digital Library

  • Sept. 12, 2015, 6:31 a.m.

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  • Jan. 19, 2016, 3:41 p.m.

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Lenhart, S.; Protopopescu, V. & Yong, J. Identification of a reflection boundary coefficient in an acoustic wave equation by optimal control techniques, article, December 31, 1997; Tennessee. (digital.library.unt.edu/ark:/67531/metadc707608/: accessed August 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.