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Volume 32, Issue 4
Static Regime Imaging of Locations of Certain 3D Electromagnetic Imperfections from a Boundary Perturbation Formula

Séraphin M. Mefire

DOI: 10.4208/jcm.1401-m4214

J. Comp. Math., 32 (2014), pp. 412-441.

Published online: 2014-08

[An open-access article; the PDF is free to any online user.]

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  • Abstract

We are concerned, in a static regime, with an imaging approach of the locations in a three-dimensional bounded domain of certain electromagnetic imperfections. This approach is related to Electrical Impedance Tomography and makes use of a new perturbation formula in the electric fields. We present two localization procedures, from a Current Projection method that deals with the single imperfection context and an inverse Fourier process that is devoted to multiple imperfections configurations. These procedures extend those that were described in our previous work, since operating for a broader class of settings. Namely, the localization is additionally performed for certain purely electric imperfections, as established from numerical simulations.

  • Keywords

Inverse problems, Maxwell equations, Electric fields, Inhomogeneities, Electrical Impedance Tomography, Current Projection method, FFT, Numerical boundary measurements, Random noise, Edge elements, Least square systems, Incomplete Modified Gram-Schmidt preconditioning.

  • AMS Subject Headings

65N21, 65N30, 78A25.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-32-412, author = {Séraphin M. Mefire}, title = {Static Regime Imaging of Locations of Certain 3D Electromagnetic Imperfections from a Boundary Perturbation Formula}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {4}, pages = {412--441}, abstract = {

We are concerned, in a static regime, with an imaging approach of the locations in a three-dimensional bounded domain of certain electromagnetic imperfections. This approach is related to Electrical Impedance Tomography and makes use of a new perturbation formula in the electric fields. We present two localization procedures, from a Current Projection method that deals with the single imperfection context and an inverse Fourier process that is devoted to multiple imperfections configurations. These procedures extend those that were described in our previous work, since operating for a broader class of settings. Namely, the localization is additionally performed for certain purely electric imperfections, as established from numerical simulations.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1401-m4214}, url = {http://global-sci.org/intro/article_detail/jcm/9895.html} }
TY - JOUR T1 - Static Regime Imaging of Locations of Certain 3D Electromagnetic Imperfections from a Boundary Perturbation Formula AU - Séraphin M. Mefire JO - Journal of Computational Mathematics VL - 4 SP - 412 EP - 441 PY - 2014 DA - 2014/08 SN - 32 DO - http://doi.org/10.4208/jcm.1401-m4214 UR - https://global-sci.org/intro/article_detail/jcm/9895.html KW - Inverse problems, Maxwell equations, Electric fields, Inhomogeneities, Electrical Impedance Tomography, Current Projection method, FFT, Numerical boundary measurements, Random noise, Edge elements, Least square systems, Incomplete Modified Gram-Schmidt preconditioning. AB -

We are concerned, in a static regime, with an imaging approach of the locations in a three-dimensional bounded domain of certain electromagnetic imperfections. This approach is related to Electrical Impedance Tomography and makes use of a new perturbation formula in the electric fields. We present two localization procedures, from a Current Projection method that deals with the single imperfection context and an inverse Fourier process that is devoted to multiple imperfections configurations. These procedures extend those that were described in our previous work, since operating for a broader class of settings. Namely, the localization is additionally performed for certain purely electric imperfections, as established from numerical simulations.

Séraphin M. Mefire. (2014). Static Regime Imaging of Locations of Certain 3D Electromagnetic Imperfections from a Boundary Perturbation Formula. Journal of Computational Mathematics. 32 (4). 412-441. doi:10.4208/jcm.1401-m4214
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