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Characterizing the shape and material properties of hidden targets from magnetic induction data

Paul Ledger, William R. B. Lionheart

IMA Journal of Applied Mathematics, Volume: 80, Issue: 6, Pages: 1776 - 1798

Swansea University Author: Paul Ledger

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DOI (Published version): 10.1093/imamat/hxv015

Abstract

The aim of this paper is to show that, for the eddy current model, the leading order term for the perturbation in the magnetic field, due to the presence of a small conducting magnetic inclusion, can be expressed in terms of a symmetric rank 2 polarization tensor. This tensor contains information ab...

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Published in: IMA Journal of Applied Mathematics
ISSN: 0272-4960 1464-3634
Published: 2015
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa22806
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Abstract: The aim of this paper is to show that, for the eddy current model, the leading order term for the perturbation in the magnetic field, due to the presence of a small conducting magnetic inclusion, can be expressed in terms of a symmetric rank 2 polarization tensor. This tensor contains information about the shape and material properties of the object and is independent of position. We apply a recently derived asymptotic formula for the perturbed magnetic field, due to the presence of a conducting inclusion, which is expressed in terms of a new class of rank 4 polarization tensors (Ammari, H., Chen, J., Chen, Z., Garnier, J. & Volkov, D. (2014) Target detection and characterization from electromagnetic induction data. J. Math. Pures Appl., 101, 54–75.) and show that their result can be written in an alternative form involving a symmetric rank 2 tensor involving 6 instead of 81 complex components in an orthonormal coordinate frame. For objects with rotational and mirror symmetries we show that the number of coefficients is still smaller. We include numerical examples to demonstrate that the new polarization tensors can be accurately computed by solving a vector-valued transmission problem by hp-finite elements and include examples to illustrate the agreement between the asymptotic formula describing the perturbed fields and the numerical predictions.
College: College of Engineering
Issue: 6
Start Page: 1776
End Page: 1798