INVERSE CONDUCTIVE MEDIUM SCATTERING WITH UNKNOWN BURIED OBJECTS*

doi:10.1007/s10473-023-0505-9

摘要/Abstract

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

Fenglong Qu, Ruixue Jia, Yanli Cui. INVERSE CONDUCTIVE MEDIUM SCATTERING WITH UNKNOWN BURIED OBJECTS^*[J]. 数学物理学报(英文版), 2023, 43(5): 2005-2025.

Fenglong Qu, Ruixue Jia, Yanli Cui. INVERSE CONDUCTIVE MEDIUM SCATTERING WITH UNKNOWN BURIED OBJECTS^*[J]. Acta mathematica scientia,Series B, 2023, 43(5): 2005-2025.

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INVERSE CONDUCTIVE MEDIUM SCATTERING WITH UNKNOWN BURIED OBJECTS^*

INVERSE CONDUCTIVE MEDIUM SCATTERING WITH UNKNOWN BURIED OBJECTS^*

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