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Volume 27, Issue 4
Three-Dimensional Numerical Localization of Imperfections Based on a Limit Model in Electric Field and a Limit Perturbation Model

S.M. Mefire

J. Comp. Math., 27 (2009), pp. 495-524.

Published online: 2009-08

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  • Abstract

From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric field for localizing numerically certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain. We introduce here two localization procedures resulting from the combination of this limit perturbation model with each of the following inversion processes: the Current Projection method and an Inverse Fourier method. Each localization procedure uses, as data, a finite number of boundary measurements, and is employed in the single inhomogeneity case; only the one based on an Inverse Fourier method is required in the multiple inhomogeneities case. Our localization approach is numerically suitable for the context of inhomogeneities that are not purely electric. We compare the numerical results obtained from the two localization procedures in the single inhomogeneity configuration, and describe, in various settings of multiple inhomogeneities, the results provided by the procedure based on an Inverse Fourier method.

  • AMS Subject Headings

65N21, 65N30, 78A25.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-495, author = {}, title = {Three-Dimensional Numerical Localization of Imperfections Based on a Limit Model in Electric Field and a Limit Perturbation Model}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {4}, pages = {495--524}, abstract = {

From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric field for localizing numerically certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain. We introduce here two localization procedures resulting from the combination of this limit perturbation model with each of the following inversion processes: the Current Projection method and an Inverse Fourier method. Each localization procedure uses, as data, a finite number of boundary measurements, and is employed in the single inhomogeneity case; only the one based on an Inverse Fourier method is required in the multiple inhomogeneities case. Our localization approach is numerically suitable for the context of inhomogeneities that are not purely electric. We compare the numerical results obtained from the two localization procedures in the single inhomogeneity configuration, and describe, in various settings of multiple inhomogeneities, the results provided by the procedure based on an Inverse Fourier method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.27.4.016}, url = {http://global-sci.org/intro/article_detail/jcm/8586.html} }
TY - JOUR T1 - Three-Dimensional Numerical Localization of Imperfections Based on a Limit Model in Electric Field and a Limit Perturbation Model JO - Journal of Computational Mathematics VL - 4 SP - 495 EP - 524 PY - 2009 DA - 2009/08 SN - 27 DO - http://doi.org/10.4208/jcm.2009.27.4.016 UR - https://global-sci.org/intro/article_detail/jcm/8586.html KW - Inverse problems, Maxwell equations, Electric fields, Inhomogeneities, Electrical Impedance Tomography, Current Projection method, FFT, Numerical boundary measurements, Edge elements, Least square systems, Incomplete Modified Gram-Schmidt preconditioning. AB -

From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric field for localizing numerically certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain. We introduce here two localization procedures resulting from the combination of this limit perturbation model with each of the following inversion processes: the Current Projection method and an Inverse Fourier method. Each localization procedure uses, as data, a finite number of boundary measurements, and is employed in the single inhomogeneity case; only the one based on an Inverse Fourier method is required in the multiple inhomogeneities case. Our localization approach is numerically suitable for the context of inhomogeneities that are not purely electric. We compare the numerical results obtained from the two localization procedures in the single inhomogeneity configuration, and describe, in various settings of multiple inhomogeneities, the results provided by the procedure based on an Inverse Fourier method.

S.M. Mefire. (2019). Three-Dimensional Numerical Localization of Imperfections Based on a Limit Model in Electric Field and a Limit Perturbation Model. Journal of Computational Mathematics. 27 (4). 495-524. doi:10.4208/jcm.2009.27.4.016
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