Characterization of Conducting Objects

Recent highlights on the characterization of hidden objects include

  • P.D. Ledger, W.R.B. Lionheart. An explicit formula for the magnetic polarizability tensor for object characterisation. IEEE Transactions on Geoscience and Remote Sensing, In print (2018). doi  10.1109/TGRS.2018.2801359.
  • P.D. Ledger, W.R.B. Lionheart. Generalised magnetic polarizability tensors. Mathematical Methods in the Applied Sciences, In print (2018) doi 10.1002/mma.4809
  • P.D. Ledger, W.R.B. Lionheart. Understanding the magnetic polarizability tensor. IEEE Transactions on Magnetics (2016) doi: 10.1109/TMAG.2015.2507169
  • P.D. Ledger, W.R.B. Lionheart. Characterizing the shape and material properties of hidden targets from magnetic induction data, IMA Journal of Applied Mathematics (2015) doi: 10.1093/imamat/hxv015

In these papers we provide a mathematical formulation for the low-cost description and characterization of highly conductive objects at low frequencies. The explicit polarization tensor description holds great promise for improving current metal detection technologies. It also provides a rigorous mathematical framework for the engineering predication. For the rank 2 case, we illustrate how topology plays an important role in the description of the objects and how the rotational and reflectional symmetries of an object can be used to reduce the number of independent coefficients and investigate the frequency, permeability and conductivity dependence of the tensor coefficients.

A MATLAB program for computing the rank 2 magnetic polarization tensor for different objects is available here.

hp-FEM Simulation of Coupled Problems

Recent highlights on the accurate computation simulation of coupled problems include

  • S. Bagwell, P.D. Ledger, A.J. Gill, M. Mallett. Transient solutions to non-linear acouto-magneto-mechanical coupling for axisymmetric MRI scanner design. Submitted (2017). Preprint.
  • S. Bagwell, P.D. Ledger, A.J. Gil, M. Mallett, M. Kruip. A linearised hp-finite element framework for acouto-magneto-mechanical coupling in axisymmetric MRI scanners. International Journal for Numerical Methods in Engineering (2017) doi: 10.1002/nme.5559
  • D. Jin, P.D. Ledger, A.J. Gil.  hp-Finite element solution of coupled stationary magnetohydrodynamics problems including magnetostrictive effects. Computers & Structures (2016) doi:10.1016/j.compstruc.2015.11.008
  • D. Jin, P.D. Ledger, A.J. Gil  An hp-fem framework for the simulation of electrostrictive and magnetostrictive materials. Computers & Structures (2014) doi:10.1016/j.compstruc.2013.10.009

These papers address applications in simulating vibrations in MRI scanners and in the behaviour of magnetic fluids and solids. The papers adopt a consistent linearisation of the governing systems of non-linear equations and solution process based on the Newton-Raphson algorithm giving quadratic convergence of the residual. The fields are discretised by a hp-finite element method, which allows for both polynomial enrichment and element subdivision leading to exponential convergence of the fields. The fields are discretised with basis functions chosen according to the nature of the weak form and ensuring a mathematically and physically correct solution. 

For more details on this work see the webpage of my PhD student Scott Bagwell.

Full Publication List

A complete list of around 30 publications can be found on

Former PhD Students

  • Massoud Zolgharni, now a Senior Lecturer in Computer Science at The University of Lincoln, UK. PhD Thesis.
  • Darong Jin, now working for Rockfield Software, UK. PhD Thesis.
  • Robin Priewald, now working for  Bright Red Systems, Austria.