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Numerical algorithm for two-dimensional inverse acoustic problem based on Gel'fand–Levitan–Krein equation
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Sergey I. Kabanikhin
and
Maxim A. Shishlenin
Published/Copyright:
April 2, 2011
Abstract
The inverse problem for the acoustic equation is considered. We propose a method of reconstruction of the density approximating 2D inverse acoustic problem by a finite system of one dimensional inverse acoustic problems. The 2D analogy of the Gel'fand–Levitan–Krein method is established. The inverse acoustic problem is formulated and the short outline of the history and development in this field are given in Section 1. In Section 2 we consider the 2D analogy of the Gel'fand–Levitan–Krein equation. The N-approximation of the Gel'fand–Levitan–Krein equation is obtained for inverse acoustic problem in Section 3. The numerical results are presented in Section 4.
Received: 2010-06-09
Published Online: 2011-04-02
Published in Print: 2011-March
© de Gruyter 2011
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- On a class of finite difference methods for ill-posed Cauchy problems with noisy data
- Numerical algorithm for two-dimensional inverse acoustic problem based on Gel'fand–Levitan–Krein equation
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Keywords for this article
Inverse acoustic problem;
Gel'fand–Levitan–Krein equation;
numerical methods
Articles in the same Issue
- Recent advances in analytical and numerical methods in inverse problems for PDEs (minisymposium report)
- On a class of finite difference methods for ill-posed Cauchy problems with noisy data
- Numerical algorithm for two-dimensional inverse acoustic problem based on Gel'fand–Levitan–Krein equation
- Some regularization methods for a thermoacoustic inverse problem
- Application of inversion methods in solving ill-posed problems for magnetic parameter identification of steel hull vessel
- On sequential minimization of Tikhonov functionals in ill-posed problems with a priori information on solutions
