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...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[1]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.展开更多
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous cavity.We shall develop a modified factorization method to reconstruct the shape and location of the i...This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous cavity.We shall develop a modified factorization method to reconstruct the shape and location of the interior interface of the inhomogeneous cavity by means of many internal measurements of the near-field data.Numerical examples are carried out to illustrate the practicability of the inversion algorithm.展开更多
Consider the inverse scattering of time-harmonic acoustic waves by a mixed-type scatterer consisting of an inhomogeneous penetrable medium with a conductive transmission condition and various impenetrable obstacles wi...Consider the inverse scattering of time-harmonic acoustic waves by a mixed-type scatterer consisting of an inhomogeneous penetrable medium with a conductive transmission condition and various impenetrable obstacles with different kinds of boundary conditions.Based on the establishment of the well-posedness result of the direct problem,we intend to develop a modified factorization method to simultaneously reconstruct both the support of the inhomogeneous conductive medium and the shape and location of various impenetrable obstacles by means of the far-field data for all incident plane waves at a fixed wave number.Numerical examples are carried out to illustrate the feasibility and effectiveness of the proposed inversion algorithms.展开更多
基金supported by the National Natural ScienceFoundation of China Grant(11871416,12171057)the Natural Science Foundation of Shandong Province Grant(ZR2019MA027)。
文摘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[1]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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11871416,12171057)by the Natural Science Foundation of Shandong Province(Grant No.ZR2019MA027)+1 种基金supported by the National Natural Science Foundation of China(Grant Nos.11971273,12126426)by the Natural Science Foundation of Shandong Province(Grant No.ZR2018MA004).
文摘This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous cavity.We shall develop a modified factorization method to reconstruct the shape and location of the interior interface of the inhomogeneous cavity by means of many internal measurements of the near-field data.Numerical examples are carried out to illustrate the practicability of the inversion algorithm.
基金supported by the National Natural Science Foundation of China Grant(Grant Nos.11871416,12171057)by the Natural Science Foundation of Shandong Province(Grant No.ZR2019MA027).
文摘Consider the inverse scattering of time-harmonic acoustic waves by a mixed-type scatterer consisting of an inhomogeneous penetrable medium with a conductive transmission condition and various impenetrable obstacles with different kinds of boundary conditions.Based on the establishment of the well-posedness result of the direct problem,we intend to develop a modified factorization method to simultaneously reconstruct both the support of the inhomogeneous conductive medium and the shape and location of various impenetrable obstacles by means of the far-field data for all incident plane waves at a fixed wave number.Numerical examples are carried out to illustrate the feasibility and effectiveness of the proposed inversion algorithms.
