### Electronic Research Archive

2023, Issue 6: 3322-3342. doi: 10.3934/era.2023168
Research article

# A hybrid method for the interior inverse scattering problem

• 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.

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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• 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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