Numerical resolution of an electromagnetic inverse medium problem at fixed frequency

The aim of this paper is to solve numerically the inverse problem of determining the complex refractive index of an electromagnetic medium from partial boundary field measurements at a fixed frequency. The governing equations are the time-harmonic Maxwell equations formulated in electric field in a...

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Veröffentlicht in:	Computers & mathematics with applications (1987) Jg. 74; H. 12; S. 3111 - 3128
Hauptverfasser:	de Buhan, M., Darbas, M.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Oxford Elsevier Ltd 15.12.2017 Elsevier BV Elsevier
Schlagworte:	Adaptive eigenspace method Algorithms Computer Science Cost functional Eigenvectors Electric fields Experiments Inverse medium problem Inverse problems Iterative methods Mathematical analysis Maxwell's equations Minimization iterative process Modeling and Simulation Nonlinear equations Numerical prediction Numerical reconstruction Optimization Reconstruction Refractivity Thermal expansion Inverse medium problem Numerical reconstruction Minimization iterative process Cost functional Adaptive eigenspace method Maxwell’s equations cost functional Maxwell's equations numerical reconstruction minimization iterative process Adaptive Eigenspace Method
ISSN:	0898-1221, 1873-7668
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Abstract	The aim of this paper is to solve numerically the inverse problem of determining the complex refractive index of an electromagnetic medium from partial boundary field measurements at a fixed frequency. The governing equations are the time-harmonic Maxwell equations formulated in electric field in a two-dimensional bounded domain. We express the inverse problem as the minimization of a cost function representing the difference between the measured and predicted fields. Our numerical reconstruction algorithm combines the BFGS method and an iterative process, called the Adaptive Eigenspace Inversion. The unknown complex coefficient is expanded in terms of eigenfunctions of an elliptic operator. Both the eigenspace and the mesh are iteratively adapted during the minimization procedure. Numerical experiments illustrate the performance of the reconstruction for various configurations.
AbstractList	The aim of this paper is to solve numerically the inverse problem of determining the complex refractive index of an electromagnetic medium from partial boundary field measurements at a fixed frequency. The governing equations are the time-harmonic Maxwell equations formulated in electric field in a two-dimensional bounded domain. We express the inverse problem as the minimization of a cost function representing the difference between the measured and predicted fields. Our numerical reconstruction algorithm combines the BFGS method and an iterative process, called the Adaptive Eigenspace Inversion. The unknown complex coefficient is expanded in terms of eigenfunctions of an elliptic operator. Both the eigenspace and the mesh are iteratively adapted during the minimization procedure. Numerical experiments illustrate the performance of the reconstruction for various configurations. The aim of this paper is to solve numerically the inverse problem of determining the complex refractive index of an electromagnetic medium from partial boundary field measurements at a fixed frequency. The governing equations are the time-harmonic Maxwell equations formulated in electric field in a two-dimensional bounded domain. We express the inverse problem as the minimization of a cost function representing the difference between the measured and predicted fields. Our numerical reconstruction algorithm combines the BFGS method and an iterative process, called the Adaptive Eigenspace Inversion. The unknown complex coefficient is expanded in terms of eigenfunctions of an elliptic operator. Both the elgenspace and the mesh are iteratively adapted during the minimization procedure. Numerical experiments illustrate the performance of the reconstruction for various configurations.
Author	de Buhan, M. Darbas, M.
Author_xml	– sequence: 1 givenname: M. surname: de Buhan fullname: de Buhan, M. organization: CNRS, UMR 8145, MAP5, Université Paris Descartes, Sorbonne Paris Cité, France – sequence: 2 givenname: M. surname: Darbas fullname: Darbas, M. email: marion.darbas@u-picardie.fr organization: CNRS UMR 7352, LAMFA, Université de Picardie Jules Verne, Amiens, France
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Keywords	Inverse medium problem Numerical reconstruction Minimization iterative process Cost functional Adaptive eigenspace method Maxwell’s equations cost functional Maxwell's equations numerical reconstruction minimization iterative process Adaptive Eigenspace Method
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Snippet	The aim of this paper is to solve numerically the inverse problem of determining the complex refractive index of an electromagnetic medium from partial...
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SubjectTerms	Adaptive eigenspace method Algorithms Computer Science Cost functional Eigenvectors Electric fields Experiments Inverse medium problem Inverse problems Iterative methods Mathematical analysis Maxwell's equations Minimization iterative process Modeling and Simulation Nonlinear equations Numerical prediction Numerical reconstruction Optimization Reconstruction Refractivity Thermal expansion
Title	Numerical resolution of an electromagnetic inverse medium problem at fixed frequency
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