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

Ledger, Paul D and Lionheart, William RB (2013) Characterising the shape and material properties of hidden targets from magnetic induction data. [MIMS Preprint]

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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 (H. Ammari, J. Chen, Z. Chen, J. Garnier and D. Volkov (2014) Target detection and characterization from electromagnetic induction data, Journal de Mathématiques Pures et Appliquées 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.

Item Type: MIMS Preprint
Additional Information: Accepted for IMA Journal of Applied Mathematics
Uncontrolled Keywords: Metal detectors, Land mine detection, Polarisation tensors, Eddy currents, hp-Finite elements
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 41 Approximations and expansions
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 41 Electromagnetism; electron and ion optics
Depositing User: Prof WRB Lionheart
Date Deposited: 03 Jun 2015
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2303

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