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Volume 33, Issue 3
Numerical Reconstruction of Locally Rough Surfaces with a Newton Iterative Algorithm

Meng Liu & Jiaqing Yang

DOI: 10.4208/cicp.OA-2022-0171

Commun. Comput. Phys., 33 (2023), pp. 884-911.

Published online: 2023-04

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  • Abstract

In this paper, we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves. The algorithm relies on the Fréchet differentiability analysis of the locally rough surface scattering problem, which is established by reducing the original model into an equivalent boundary value problem with compactly supported boundary data. With a slight modification, the algorithm can be also extended to reconstruct the local perturbation of a non-local rough surface. Finally, numerical results are presented to illustrate the effectiveness of the inversion algorithm with the multi-frequency data.

  • Keywords

Newton iterative algorithm, Fréchet derivative, inverse scattering, locally rough surface, Dirichlet condition, impedance condition, multi-frequency data.

  • AMS Subject Headings

35R30, 35J05, 35P25, 65N21

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-33-884, author = {Liu , Meng and Yang , Jiaqing}, title = {Numerical Reconstruction of Locally Rough Surfaces with a Newton Iterative Algorithm}, journal = {Communications in Computational Physics}, year = {2023}, volume = {33}, number = {3}, pages = {884--911}, abstract = {

In this paper, we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves. The algorithm relies on the Fréchet differentiability analysis of the locally rough surface scattering problem, which is established by reducing the original model into an equivalent boundary value problem with compactly supported boundary data. With a slight modification, the algorithm can be also extended to reconstruct the local perturbation of a non-local rough surface. Finally, numerical results are presented to illustrate the effectiveness of the inversion algorithm with the multi-frequency data.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0171}, url = {http://global-sci.org/intro/article_detail/cicp/21663.html} }
TY - JOUR T1 - Numerical Reconstruction of Locally Rough Surfaces with a Newton Iterative Algorithm AU - Liu , Meng AU - Yang , Jiaqing JO - Communications in Computational Physics VL - 3 SP - 884 EP - 911 PY - 2023 DA - 2023/04 SN - 33 DO - http://doi.org/10.4208/cicp.OA-2022-0171 UR - https://global-sci.org/intro/article_detail/cicp/21663.html KW - Newton iterative algorithm, Fréchet derivative, inverse scattering, locally rough surface, Dirichlet condition, impedance condition, multi-frequency data. AB -

In this paper, we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves. The algorithm relies on the Fréchet differentiability analysis of the locally rough surface scattering problem, which is established by reducing the original model into an equivalent boundary value problem with compactly supported boundary data. With a slight modification, the algorithm can be also extended to reconstruct the local perturbation of a non-local rough surface. Finally, numerical results are presented to illustrate the effectiveness of the inversion algorithm with the multi-frequency data.

Liu , Meng and Yang , Jiaqing. (2023). Numerical Reconstruction of Locally Rough Surfaces with a Newton Iterative Algorithm. Communications in Computational Physics. 33 (3). 884-911. doi:10.4208/cicp.OA-2022-0171
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