A hybrid method for the interior inverse scattering problem

Yujie Wang; Enxi Zheng; Wenyan Wang; Yujie Wang; Enxi Zheng; Wenyan Wang

doi:10.3934/era.2023168

Electronic Research Archive

2023, Volume 31, Issue 6: 3322-3342. doi: 10.3934/era.2023168

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Research article

A hybrid method for the interior inverse scattering problem

School of Science, Dalian Maritime University, No. 1 of Linghai Road, Dalian 116026, Liaoning, China

Received: 07 February 2023 Revised: 26 March 2023 Accepted: 03 April 2023 Published: 12 April 2023

In this paper, the interior inverse scattering problem of a cavity is considered. By use of a general boundary condition, we can reconstruct the shape of the cavity without a priori information of the boundary condition type. The method of fundamental solutions (MFS) with regularization is formulated for solving the scattered field and its normal derivative on the cavity boundary. Newton's method is employed to reconstruct the cavity boundary by satisfying the general boundary condition. This hybrid method copes with the ill-posedness of the inverse problem in the MFS step and deals with the nonlinearity in the Newton's step. Some computational examples are presented to demonstrate the effectiveness of our method.
- hybrid method,
- inverse cavity problem,
- method of fundamental solutions,
- interior scattering,
- unknown boundary condition
Citation: Yujie Wang, Enxi Zheng, Wenyan Wang. A hybrid method for the interior inverse scattering problem[J]. Electronic Research Archive, 2023, 31(6): 3322-3342. doi: 10.3934/era.2023168

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Abstract

In this paper, the interior inverse scattering problem of a cavity is considered. By use of a general boundary condition, we can reconstruct the shape of the cavity without a priori information of the boundary condition type. The method of fundamental solutions (MFS) with regularization is formulated for solving the scattered field and its normal derivative on the cavity boundary. Newton's method is employed to reconstruct the cavity boundary by satisfying the general boundary condition. This hybrid method copes with the ill-posedness of the inverse problem in the MFS step and deals with the nonlinearity in the Newton's step. Some computational examples are presented to demonstrate the effectiveness of our method.

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