数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (5): 2005-2025.doi: 10.1007/s10473-023-0505-9

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INVERSE CONDUCTIVE MEDIUM SCATTERING WITH UNKNOWN BURIED OBJECTS*

Fenglong Qu, Ruixue Jia, Yanli Cui   

  1. School of Mathematics and Information Sciences, Yantai University, Yantai 264005, China
  • 收稿日期:2022-03-10 修回日期:2023-04-26 发布日期:2023-10-25

INVERSE CONDUCTIVE MEDIUM SCATTERING WITH UNKNOWN BURIED OBJECTS*

Fenglong Qu, Ruixue Jia, Yanli Cui   

  1. School of Mathematics and Information Sciences, Yantai University, Yantai 264005, China
  • Received:2022-03-10 Revised:2023-04-26 Published:2023-10-25
  • Contact: †Fenglong Qu, E-mail: fenglongqu@amss.ac.cn
  • About author:Ruixue Jia, E-mail: jiarx6258@163.com; Yanli Cui, E-mail: cuiyanli@ytu.edu.cn
  • Supported by:
    National Natural Science Foundation of China Grant (11871416, 12171057) and the Natural Science Foundation of Shandong Province Grant (ZR2019MA027).

摘要: This paper is concerned with inverse acoustic scattering in an inhomogeneous medium with a conductive boundary condition and the unknown buried impenetrable objects inside. Using a variational approach, we establish the well-posedness of the direct problem. For the inverse problem, we shall numerically reconstruct the inhomogeneous medium from the far-field data for different kinds of cases. For the case when a Dirichlet boundary condition is imposed on the buried object, the classical factorization method proposed in [2] is justified as valid for reconstructing the inhomogeneous medium from the far-field data. For the case when a Neumann boundary condition is imposed on the buried object, the classical factorization method of [1] cannot be applied directly, since the middle operator of the factorization of the far-field operator is only compact. In this case, we develop a modified factorization method to locate the inhomogeneous medium with a conductive boundary condition and the unknown buried objects. Some numerical experiments are provided to demonstrate the practicability of the inversion algorithms developed.

关键词: inverse acoustic scattering, factorization method, numerical reconstruction, inhomogeneous medium

Abstract: This paper is concerned with inverse acoustic scattering in an inhomogeneous medium with a conductive boundary condition and the unknown buried impenetrable objects inside. Using a variational approach, we establish the well-posedness of the direct problem. For the inverse problem, we shall numerically reconstruct the inhomogeneous medium from the far-field data for different kinds of cases. For the case when a Dirichlet boundary condition is imposed on the buried object, the classical factorization method proposed in [2] is justified as valid for reconstructing the inhomogeneous medium from the far-field data. For the case when a Neumann boundary condition is imposed on the buried object, the classical factorization method of [1] cannot be applied directly, since the middle operator of the factorization of the far-field operator is only compact. In this case, we develop a modified factorization method to locate the inhomogeneous medium with a conductive boundary condition and the unknown buried objects. Some numerical experiments are provided to demonstrate the practicability of the inversion algorithms developed.

Key words: inverse acoustic scattering, factorization method, numerical reconstruction, inhomogeneous medium

中图分类号: 

  • 35R30