Simultaneous reconstruction of the shape and surface impedance from Cauchy data for the Helmholtz equation

In this paper, we are concerned with the coefficients identification for the Helmholtz equation. This problem consists of determining the shape and surface impedance from boundary Cauchy data. We propose two reconstruction algorithms to simultaneously recover the shape and the surface impedance of t...

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Bibliographic Details
Published inOptimization Vol. 74; no. 7; pp. 1573 - 1589
Main Author Liu, Ji-Chuan
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 19.05.2025
Taylor & Francis LLC
Subjects
Algorithms
Helmholtz equation
Helmholtz equations
ill-posed problem
Impedance
Levenberg-Marquardt algorithm
Optimization algorithms
Reconstruction
Regularization
Regularization methods
trust-region-reflective optimization algorithm
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ISSN0233-1934
1029-4945
DOI10.1080/02331934.2024.2318251

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Summary:In this paper, we are concerned with the coefficients identification for the Helmholtz equation. This problem consists of determining the shape and surface impedance from boundary Cauchy data. We propose two reconstruction algorithms to simultaneously recover the shape and the surface impedance of the obstacle within a body. This problem is ill-posed, thus we apply regularization techniques in order to improve the corresponding approximation. The numerical results show that the proposed algorithms are stable and effective.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2024.2318251