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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
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URI: https://cronfa.swan.ac.uk/Record/cronfa22806
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spelling 2019-06-27T10:34:36.5488367 v2 22806 2015-08-06 Characterizing the shape and material properties of hidden targets from magnetic induction data 068dd31af167bcda33878951b2a01e97 Paul Ledger Paul Ledger true false 2015-08-06 FGSEN 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. Journal Article IMA Journal of Applied Mathematics 80 6 1776 1798 0272-4960 1464-3634 31 12 2015 2015-12-31 10.1093/imamat/hxv015 http://imamat.oxfordjournals.org/content/early/2015/06/25/imamat.hxv015 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2019-06-27T10:34:36.5488367 2015-08-06T18:10:53.3425455 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Paul Ledger 1 William R. B. Lionheart 2 0022806-17092015094536.pdf IMA__J__Appl__Math-2015-Ledger-imamat_hxv015.pdf 2015-09-17T09:45:36.3730000 Output 860265 application/pdf Version of Record true 2015-09-15T00:00:00.0000000 Distributed under the terms of a Creative Commons Attribution Non-Commercial (CC-BY-3.0) true
title Characterizing the shape and material properties of hidden targets from magnetic induction data
spellingShingle Characterizing the shape and material properties of hidden targets from magnetic induction data
Paul Ledger
title_short Characterizing the shape and material properties of hidden targets from magnetic induction data
title_full Characterizing the shape and material properties of hidden targets from magnetic induction data
title_fullStr Characterizing the shape and material properties of hidden targets from magnetic induction data
title_full_unstemmed Characterizing the shape and material properties of hidden targets from magnetic induction data
title_sort Characterizing the shape and material properties of hidden targets from magnetic induction data
author_id_str_mv 068dd31af167bcda33878951b2a01e97
author_id_fullname_str_mv 068dd31af167bcda33878951b2a01e97_***_Paul Ledger
author Paul Ledger
author2 Paul Ledger
William R. B. Lionheart
format Journal article
container_title IMA Journal of Applied Mathematics
container_volume 80
container_issue 6
container_start_page 1776
publishDate 2015
institution Swansea University
issn 0272-4960
1464-3634
doi_str_mv 10.1093/imamat/hxv015
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
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department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
url http://imamat.oxfordjournals.org/content/early/2015/06/25/imamat.hxv015
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description 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.
published_date 2015-12-31T03:24:38Z
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