Volume 26, Issue 2
Numerical Localization of Electromagnetic Imperfections from a Perturbation Formula in Three Dimensions

M. Asch & S. M. Mefire

DOI:

J. Comp. Math., 26 (2008), pp. 149-195

Published online: 2008-04

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  • Abstract

This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms: the Current Projection method, the MUltiple SIgnal Classification (MUSIC) algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings.

  • Keywords

Inverse problems Maxwell equations Electric fields Three-dimensional inhomogeneities Electrical impedance tomography Current projection method MUSIC algorithm FFT Edge elements Numerical boundary measurements

  • AMS Subject Headings

35R30 65N21 65N30 78A25.

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COPYRIGHT: © Global Science Press

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@Article{JCM-26-149, author = {}, title = {Numerical Localization of Electromagnetic Imperfections from a Perturbation Formula in Three Dimensions}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {2}, pages = {149--195}, abstract = { This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms: the Current Projection method, the MUltiple SIgnal Classification (MUSIC) algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings.}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8617.html} }
TY - JOUR T1 - Numerical Localization of Electromagnetic Imperfections from a Perturbation Formula in Three Dimensions JO - Journal of Computational Mathematics VL - 2 SP - 149 EP - 195 PY - 2008 DA - 2008/04 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8617.html KW - Inverse problems KW - Maxwell equations KW - Electric fields KW - Three-dimensional inhomogeneities KW - Electrical impedance tomography KW - Current projection method KW - MUSIC algorithm KW - FFT KW - Edge elements KW - Numerical boundary measurements AB - This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms: the Current Projection method, the MUltiple SIgnal Classification (MUSIC) algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings.
M. Asch & S. M. Mefire. (1970). Numerical Localization of Electromagnetic Imperfections from a Perturbation Formula in Three Dimensions. Journal of Computational Mathematics. 26 (2). 149-195. doi:
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