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The spectral properties of the magnetic polarizability tensor for metallic object characterisation (2019)
Journal Article
Ledger, P., & Lionheart, W. (2020). The spectral properties of the magnetic polarizability tensor for metallic object characterisation. Mathematical Methods in the Applied Sciences, 43(1), 78-113. https://doi.org/10.1002/mma.5830

The measurement of time-harmonic perturbed field data, at a range of frequencies, is beneficial for practical metal detection, where the goal is to locate and identify hidden targets. In particular, these benefits are realised when frequency-dependen... Read More about The spectral properties of the magnetic polarizability tensor for metallic object characterisation.

An accurate and efficient three‐dimensional high‐order finite element methodology for the simulation of magneto‐mechanical coupling in MRI scanners (2019)
Journal Article
Seoane, M., Ledger, P., Gil, A., & Mallett, M. (2019). An accurate and efficient three‐dimensional high‐order finite element methodology for the simulation of magneto‐mechanical coupling in MRI scanners. International Journal for Numerical Methods in Engineering, 119(12), 1185-1215. https://doi.org/10.1002/nme.6088

Transient magnetic fields are generated by the gradient coils in an magnetic resonance imaging (MRI) scanner and induce eddy currents in their conducting components, which lead to vibrations, imaging artefacts, noise, and the dissipation of heat. Hea... Read More about An accurate and efficient three‐dimensional high‐order finite element methodology for the simulation of magneto‐mechanical coupling in MRI scanners.

Accelerating magnetic induction tomography‐based imaging through heterogeneous parallel computing (2019)
Journal Article
Walker, D. W., Kramer, S. C., Biebl, F. R. A., Ledger, P. D., & Brown, M. (in press). Accelerating magnetic induction tomography‐based imaging through heterogeneous parallel computing. Concurrency and Computation: Practice and Experience, e5265. https://doi.org/10.1002/cpe.5265

Magnetic Induction Tomography (MIT) is a non-invasive imaging technique, which has applications in both industrial and clinical settings. In essence, it is capable of reconstructing the electromagnetic parameters of an object from measurements made o... Read More about Accelerating magnetic induction tomography‐based imaging through heterogeneous parallel computing.

Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors (2018)
Journal Article
Ledger, P. D., Lionheart, W. R. B., & Amad, A. A. S. (2019). Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors. Mathematical Methods in the Applied Sciences, 42(3), 830-860. https://doi.org/10.1002/mma.5387

Realistic applications in metal detection involve multiple inhomogeneous-conducting permeable objects, and the aim of this paper is to characterise such objects by polarizability tensors. We show that, for the eddy current model, the leading order te... Read More about Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors.

Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design: Transient nonlinear acousto-magneto-mechanical coupling in MRI (2018)
Journal Article
Bagwell, S., Ledger, P., Gil, A., & Mallett, M. (2018). Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design: Transient nonlinear acousto-magneto-mechanical coupling in MRI. International Journal for Numerical Methods in Engineering, 115(2), 209-237. https://doi.org/10.1002/nme.5802

In this work, we simulate the coupled physics describing a magnetic resonance imaging (MRI) scanner by using a higher-order finite element discretisation and a Newton-Raphson algorithm. To apply the latter, a linearisation of the nonlinear system of... Read More about Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design: Transient nonlinear acousto-magneto-mechanical coupling in MRI.

An Explicit Formula for the Magnetic Polarizability Tensor for Object Characterization (2018)
Journal Article
Ledger, P. D., & Lionheart, W. R. B. (2018). An Explicit Formula for the Magnetic Polarizability Tensor for Object Characterization. IEEE Transactions on Geoscience and Remote Sensing, 56(6), 3520-3533. https://doi.org/10.1109/tgrs.2018.2801359

The magnetic polarizability tensor (MPT) has attracted considerable interest due to the possibility it offers for characterizing conducting objects and assisting with the identification and location of hidden targets in metal detection. An explicit f... Read More about An Explicit Formula for the Magnetic Polarizability Tensor for Object Characterization.

A linearisedhp-finite element framework for acousto-magneto-mechanical coupling in axisymmetric MRI scanners: ACOUSTO-MAGNETO-MECHANICAL COUPLING IN MRI SCANNERS (2017)
Journal Article
Bagwell, S., Ledger, P. D., Gil, A. J., Mallett, M., & Kruip, M. (2017). A linearisedhp-finite element framework for acousto-magneto-mechanical coupling in axisymmetric MRI scanners: ACOUSTO-MAGNETO-MECHANICAL COUPLING IN MRI SCANNERS. International Journal for Numerical Methods in Engineering, 112(10), 1323-1352. https://doi.org/10.1002/nme.5559

We propose a new computational framework for the treatment of acousto-magneto-mechanical coupling that arises in low-frequency electro-magneto-mechanical systems such as magnetic resonance imaging scanners. Our transient Newton–Raphson strategy invol... Read More about A linearisedhp-finite element framework for acousto-magneto-mechanical coupling in axisymmetric MRI scanners: ACOUSTO-MAGNETO-MECHANICAL COUPLING IN MRI SCANNERS.

Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems (2017)
Journal Article
Kynch, R., & Ledger, P. (2017). Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems. Computers and Structures, 181, 41-54. https://doi.org/10.1016/j.compstruc.2016.05.021

A procedure for addressing the sign conflict issue for conforming hexahedral meshes.An efficient implementation of hierarchic hp-Nedelec elements in deal.II.Solution of a series of challenging 3D eddy current benchmark problems.Description of the ext... Read More about Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems.

Magnetic polarizability tensors for low frequency object classification and detection (2017)
Presentation / Conference
Ledger, P. D., & Lionheart, W. R. B. (2017, March). Magnetic polarizability tensors for low frequency object classification and detection. Paper presented at 2017 International Applied Computational Electromagnetics Society Symposium - Italy (ACES), Florence

There is considerable interest in obtaining a low-cost mathematical description, which describes the interaction between a low frequency alternating magnetic field and a conducting object. Electrical engineers have proposed that the voltage perturbat... Read More about Magnetic polarizability tensors for low frequency object classification and detection.

hp-Finite element solution of coupled stationary magnetohydrodynamics problems including magnetostrictive effects (2016)
Journal Article
Jin, D., Ledger, P., & Gil, A. (2016). hp-Finite element solution of coupled stationary magnetohydrodynamics problems including magnetostrictive effects. Computers and Structures, 164, 161-180. https://doi.org/10.1016/j.compstruc.2015.11.008

The first computational treatment of magnetostritive effects in conducting fluids.Consistent linearisation of the coupled non-linear equations.Computational solution using Newton-Raphson and hp-finite elements.Benchmarking against problems with homog... Read More about hp-Finite element solution of coupled stationary magnetohydrodynamics problems including magnetostrictive effects.

Understanding the magnetic polarizability tensor (2015)
Journal Article
Ledger, P. D., & Lionheart, W. R. B. (2016). Understanding the magnetic polarizability tensor. IEEE Transactions on Magnetics, 52(5), 1-16. https://doi.org/10.1109/tmag.2015.2507169

The aim of this paper is to provide new insights into the properties of the rank 2 polarizability tensor M̆ proposed by Ledger and Lionheart for describing the perturbation in the magnetic field caused by the presence of a conducting object in the ed... Read More about Understanding the magnetic polarizability tensor.

Solution of an industrially relevant coupled magneto–mechanical problem set on an axisymmetric domain (2015)
Journal Article
Ledger, P. D., Gil, A. J., Poya, R., Kruip, M., Wilkinson, I., & Bagwell, S. (2016). Solution of an industrially relevant coupled magneto–mechanical problem set on an axisymmetric domain. Applied Mathematical Modelling, 40(3), 1959-1971. https://doi.org/10.1016/j.apm.2015.09.030

Eddy currents are generated when low frequency magnetic fields interact with conducting components and this, in turn, generates Lorentz forces, which can cause these metallic components to deform and vibrate. An important application of this magneto–... Read More about Solution of an industrially relevant coupled magneto–mechanical problem set on an axisymmetric domain.

Characterizing the shape and material properties of hidden targets from magnetic induction data (2015)
Journal Article
Ledger, P. D., & Lionheart, W. R. B. (in press). Characterizing the shape and material properties of hidden targets from magnetic induction data. IMA Journal of Applied Mathematics, hxv015. https://doi.org/10.1093/imamat/hxv015

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 polari... Read More about Characterizing the shape and material properties of hidden targets from magnetic induction data.

A computational framework for the analysis of linear piezoelectric beams using hp-FEM (2015)
Journal Article
Poya, R., Gil, A. J., & Ledger, P. D. (2015). A computational framework for the analysis of linear piezoelectric beams using hp-FEM. Computers and Structures, 152, 155-172. https://doi.org/10.1016/j.compstruc.2015.01.012

A new computational framework for 3D linear piezoelectric beams using hp-FEM.Framework suitable for statics, dynamics, actuation and energy harvesting problems.Framework suitable for any anisotropy or electric polarisation orientation.New set of beam... Read More about A computational framework for the analysis of linear piezoelectric beams using hp-FEM.

The perturbation of electromagnetic fields at distances that are large compared with the object's size (2014)
Journal Article
Ledger, P. D., & Lionheart, W. R. B. (2015). The perturbation of electromagnetic fields at distances that are large compared with the object's size. IMA Journal of Applied Mathematics, 80(3), 865-892. https://doi.org/10.1093/imamat/hxu009

We rigorously derive the leading-order terms in asymptotic expansions for the scattered electric and magnetic fields in the presence of a small object at distances that are large compared with its size. Our expansions hold for fixed wavenumber when t... Read More about The perturbation of electromagnetic fields at distances that are large compared with the object's size.

An hp-fem framework for the simulation of electrostrictive and magnetostrictive materials (2013)
Journal Article
Jin, D., Ledger, P., & Gil, A. (2014). An hp-fem framework for the simulation of electrostrictive and magnetostrictive materials. Computers and Structures, 133, 131-148. https://doi.org/10.1016/j.compstruc.2013.10.009

The physical understanding of coupled electro-magneto-mechanics has long been a topic of particular importance for scientists. However, it is only in more recent times that the computational mechanics community has been involved, due to the particula... Read More about An hp-fem framework for the simulation of electrostrictive and magnetostrictive materials.

Fast Magnetic Flux Leakage Signal Inversion for the Reconstruction of Arbitrary Defect Profiles in Steel Using Finite Elements (2012)
Journal Article
Priewald, R. H., Magele, C., Ledger, P. D., Pearson, N. R., & Mason, J. S. D. (2013). Fast Magnetic Flux Leakage Signal Inversion for the Reconstruction of Arbitrary Defect Profiles in Steel Using Finite Elements. IEEE Transactions on Magnetics, 49(1), 506-516. https://doi.org/10.1109/tmag.2012.2208119

This paper proposes a fast and effective method for reconstructing arbitrary defect profiles in steel plates from magnetic flux leakage (MFL) measurements widely used in nondestructive testing (NDT) of oil storage tanks and pipelines. The inverse rec... Read More about Fast Magnetic Flux Leakage Signal Inversion for the Reconstruction of Arbitrary Defect Profiles in Steel Using Finite Elements.