Year: 2021
Author: Yuqing Hu
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 6 : pp. 1558–1574
Abstract
Consider the inverse scattering problem in terms of Helmholtz equation. We study a simply connected domain with oblique derivative boundary condition. In the case of constant $\lambda$, given a finite number of incident wave, the shape of the scatterer is reconstructed from the measured far-field data. We propose a Newton method which is based on the nonlinear boundary integral equation. After computing the Fréchet derivatives with respect to the unknown boundary, the nonlinear equation is transformed to its linear form, then we show the iteration scheme for the inverse problem. We conclude our paper by presenting several numerical examples for shape reconstruction to show the validity of the method we presented.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0039
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 6 : pp. 1558–1574
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Helmholtz equation oblique derivative problem nonlinear integral equation iterative solution numerics.