Identification of a reflection boundary coefficient in an acoustic wave equation by optimal control techniques
- Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.
- Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.
- Fudan Univ., Shanghai (China). Dept. of Mathematics
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.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States)
- DOE Contract Number:
- AC05-96OR22464
- OSTI ID:
- 677106
- Report Number(s):
- ORNL/CP-99354; CONF-9706289-; ON: DE99000202; BR: KC0401030; TRN: AHC29821%%241
- Resource Relation:
- Conference: ISAAC `97 conference, Delaware, MD (United States), 3-7 Jun 1997; Other Information: PBD: [1997]
- Country of Publication:
- United States
- Language:
- English
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