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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Bibliographic Details
Published in:Computers & mathematics with applications (1987) Vol. 74; no. 12; pp. 3111 - 3128
Main Authors: de Buhan, M., Darbas, M.
Format: Journal Article
Language:English
Published: Oxford Elsevier Ltd 15.12.2017
Elsevier BV
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2017.08.002