Biography

I work at the interface of applied mathematics, computer science and engineering and undertake research in the areas of computational mathematics, computational mechanics and data science.

I obtained my bachelors degree in the Civil Engineering with Computational Mechanics from The University of Birmingham. This was followed by an MSc in Computational Modelling and Finite Elements in Engineering Mechanics and a PhD Computational Electromagnetics from Swansea University. For my doctoral work, I was awarded the ECCOMAS prize for the Best Thesis in Computational Science and Engineering.

After finishing my doctorate, I held a number of postdoctoral positions including 2-years at the Seminar for Applied Mathematics, ETH Zurich in Switzerland. From 2006, I worked as a Lecturer and subsequently as an Associate Professor at The College of Engineering, Swansea University. In 2020 I moved to take up my current appointment at Keele University.

Qualifications

  • PhD Computational Science and Engineering, Swansea University (winner of the 2002 ECCOMAS prize for best thesis on Computational Science and Engineering)
  • MSc Computational Modelling and Finite Elements in Engineering Mechanics, Swansea University, 2001.
  • BEng Civil Engineering with Computational Mechanics, The University of Birmingham, 1998.

External Recognition

  • Honorary Associate Professor, College of Engineering, Swansea University
  • Member of the Society for Industrial and Applied Mathematics (SIAM)
  • Chartered Mathematician and Member of the Institute for Mathematics and its Applications (IMA)
  • Member of the London Mathematical Society (LMS)
  • Member of the organising committee for 1st IMA Conference on Inverse Problems from Theory to Applications
  • Reviewer for a range of journals including International Journal for Numerical Methods in Engineering, Computer Methods in Applied Mechanics and Engineering, Applied Mathematical Modelling, Computers & Structures, Computational Physics, COMPEL, Electromagnetics, IEEE Transactions on Magnetics, IEEE Transactions on Geophysics and Remote Sensing, Inverse Problems in Science and Engineering, IMA Journal on Numerical Analysis, IMA Journal on Applied Mathematics
  • Reviewer for EPSRC proposals

Research and scholarship

I have worked in the area of computational mathematics/computational mechanics for around 20 years where my initial research focus was on accurate (hp) finite element schemes in computational electromagnetism. In recent years, my interests have extended to the computational solution of inverse problems involving the identification and location of hidden objects in application areas such as metal detection and medical imaging. In this area, my current focus is on object characterisation and the statistical classification of objects, which has led to cross overs to data science where I also have a growing interest.  I have also worked extensively on the simulation of coupled magneto-mechanical problems and, in particular, to the application area of predicting eddy current induced vibrations in MRI scanners.

I am grateful to the funding I have received from RCUK grants from the EPSRC, Royal Society and the Royal Academy of Engineering, which has supported my research. Further details of the projects funded by these grants, and the impacts arising out of this funding, can be found on my personal page under further information.

I actively collaborate with other academic institutions including Cardiff University, The University of Manchester, Swansea University and University College London. I also work closely with industry including DSTL, Rapiscan Systems, Safeline and Siemens Healthineers.

Grants

  • EPSRC Response-Mode Project EP/V009028/1 (PI): Object Detection, Location and Identification at Radio Frequencies in the Near Field [joint with Professors Lionheart and Professor Law, The University of Manchester] Total value of EPSRC funding for two institutions £592,342 (August 2021-July 2024)
  • EPSRC Response-Mode Project EP/V049453/1 (PI): Generalised Magnetic Polarizability Tensors: Invariants and Symmetry Groups, [joint with Professor Lionheart, The University of Manchester] Total value of EPSRC funding for two institutions £78,310 (July 2021-June 2022)
  • EPSRC CASE Award Studentship (PI) - Machine Learning for Magnet Manufacture with Siemens Healthineers and Professor Gil, Swansea University, Value £117K. (July 2021 -June 2025)
  • EPSRC DTP Studentship 2129099 (PI) - Machine Learning for Improving Metal Detection. Value £60K. October 2018- March 2022.
  • EPSRC Response-Mode Project EP/R002134/1, EP/R002134/2 (PI): Reducing the Threat to Public Safety: Improved metallic object characterisation, location and detection [joint with Professors Lionheart, Peyton The University of Manchester and Dr Timo Betcke, UCL]. Total value of the EPSRC funding for three institutions £648K. (January 2018- December 2021)
  • EPSRC Case Award Studentship EP/L505699/1 (PI): Simulation of magneto-mechanical coupling in MRI scanners with Siemens Magnet Technology and Professor Gil, Swansea University. Total value of the EPSRC and company funding £98K. July 2014-December 2017.
  • EPSRC Response-Mode EP/K023950/1 (PI): Inverse Problems for Magnetic Induction Tomography [joint with Professors Brown, Marletta, Walker, Cardiff University]. Total value of two institutions EPSRC funding £648K. September 2013- August 2016.
  • EPSRC Mathematical Sciences Small Grant EP/K039865/1 (PI): Generalised Polarisation Tensors for Maxwell’s Equations [joint with Professor Lionheart, The University of Manchester]. Total value of EPSRC funding £22K. July 2013- July 2015.
  • EPSRC Bridging the Gaps Escalator Grant (PI): Application of hp-finite elements to the coupled Maxwell-Biot system for applications in Seismo-electric measurements [Joint with Professors Gil and Kulessa, Swansea University]. March 2012-July 2013. (£3K).
  • HESTEM project funding (PI): College of Engineering Mathematics Support Service, Swansea University. September 2011-July 2012. (£7K).
  • Swansea University small teaching grant (PI): Use of Tablet PC’s in engineering mathematics lectures. September 2011-July 2012. (£1.5K).
  • Royal Society travel grant (France) (PI). June 2012. (£1.5K).

Teaching

  • CSC-10052 Making Sense of Statistics for Data Scientists
  • MAT-10049 Investigations and Problem Solving
  • MAT-30016 Project II ISP
  • MAT-30043 Project (30 Credits)
  • MAT-40003 Masters Project

Further information

Personal Homepage of Paul Ledger
https://pdledger.wordpress.com

Google Scholar
https://scholar.google.co.uk/citations?user=uBsB3qEAAAAJ&hl=en

ORCID Profile
http://orcid.org/0000-0002-2587-7023

Selected Publications

  • Ledger PD, Wilson BA, Amad AAS, Lionheart WRB. 2021. Identification of metallic objects using spectral magnetic polarizability tensor signatures: Object characterisation and invariants. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 3941-3984, vol. 122(15). link> doi> full text>
  • Wilson BA and Ledger PD. 2021. Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1940-1963, vol. 122(8). link> doi> full text>
  • Barroso G, Seoane M, Gil AJ, Ledger PD, Mallett M, Huerta A. 2020. A staggered high-dimensional Proper Generalised Decomposition for coupled magneto-mechanical problems with application to MRI scanners. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, Article ARTN 113271, vol. 370. link> doi>
  • Seoane M, Ledger PD, Gil AJ, Zlotnik S, Mallett M. 2020. A combined reduced order-full order methodology for the solution of 3D magneto-mechanical problems with application to magnetic resonance imaging scanners. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 3529-3559, vol. 121(16). link> doi>
  • Barroso G, Gil AJ, Ledger PD, Mallett M, Huerta A. 2020. A regularised-adaptive Proper Generalised Decomposition implementation for coupled magneto-mechanical problems with application to MRI scanners. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, Article ARTN 112640, vol. 358. link> doi>

Full Publications Listshow

Journal Articles

  • Ledger PD, Wilson BA, Amad AAS, Lionheart WRB. 2021. Identification of metallic objects using spectral magnetic polarizability tensor signatures: Object characterisation and invariants. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 3941-3984, vol. 122(15). link> doi> full text>
  • Wilson BA and Ledger PD. 2021. Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1940-1963, vol. 122(8). link> doi> full text>
  • Barroso G, Seoane M, Gil AJ, Ledger PD, Mallett M, Huerta A. 2020. A staggered high-dimensional Proper Generalised Decomposition for coupled magneto-mechanical problems with application to MRI scanners. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, Article ARTN 113271, vol. 370. link> doi>
  • Seoane M, Ledger PD, Gil AJ, Zlotnik S, Mallett M. 2020. A combined reduced order-full order methodology for the solution of 3D magneto-mechanical problems with application to magnetic resonance imaging scanners. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 3529-3559, vol. 121(16). link> doi>
  • Barroso G, Gil AJ, Ledger PD, Mallett M, Huerta A. 2020. A regularised-adaptive Proper Generalised Decomposition implementation for coupled magneto-mechanical problems with application to MRI scanners. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, Article ARTN 112640, vol. 358. link> doi>
  • Ledger PD and Lionheart WRB. 2020. The spectral properties of the magnetic polarizability tensor for metallic object characterisation. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 78-113, vol. 43(1). link> doi>
  • Seoane M, Ledger PD, Gil AJ, 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, 1185-1215, vol. 119(12). link> doi>
  • Walker DW, Kramer SC, Biebl FRA, Ledger PD, Brown M. 2019. Accelerating magnetic induction tomography-based imaging through heterogeneous parallel computing. CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE, Article ARTN e5265, vol. 31(17). link> doi>
  • Ledger PD, Lionheart WRB, Amad AAS. 2019. Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 830-860, vol. 42(3). link> doi>
  • Ledger PD and Lionheart WRB. 2018. An Explicit Formula for the Magnetic Polarizability Tensor for Object Characterization. IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, 3520-3533, vol. 56(6). link> doi>
  • Bagwell S, Ledger PD, Gil AJ, Mallett M. 2018. Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 209-237, vol. 115(2). link> doi>
  • Ledger PD and Lionheart WRB. 2018. Generalised magnetic polarizability tensors. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 3175-3196, vol. 41(8). link> doi>
  • Bagwell S, Ledger PD, Gil AJ, Mallett M, Kruip M. 2017. A linearised hp-finite element framework for acousto-magneto-mechanical coupling in axisymmetric MRI scanners. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1323-1352, vol. 112(10). link> doi>
  • Kynch RM and Ledger PD. 2017. Resolving the sign conflict problem for hp-hexahedral Nedelec elements with application to eddy current problems. COMPUTERS & STRUCTURES, 41-54, vol. 181. link> doi>
  • Ledger PD and Lionheart WRB. 2016. Understanding the Magnetic Polarizability Tensor. IEEE TRANSACTIONS ON MAGNETICS, vol. 52(5). link> doi>
  • Ledger PD, Gil AJ, 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, 1959-1971, vol. 40(3). link> doi>
  • Jin D, Ledger PD, Gil AJ. 2016. hp-Finite element solution of coupled stationary magnetohydrodynamics problems including magnetostrictive effects. COMPUTERS & STRUCTURES, 161-180, vol. 164. link> doi>
  • Ledger PD and Lionheart WRB. 2015. Characterizing the shape and material properties of hidden targets from magnetic induction data. IMA JOURNAL OF APPLIED MATHEMATICS, 1776-1798, vol. 80(6). link> doi>
  • Poya R, Gil AJ, Ledger PD. 2015. A computational framework for the analysis of linear piezoelectric beams using hp-FEM. COMPUTERS & STRUCTURES, 155-172, vol. 152. link> doi>
  • Ledger PD and Lionheart WRB. 2015. The perturbation of electromagnetic fields at distances that are large compared with the object's size. IMA JOURNAL OF APPLIED MATHEMATICS, 865-892, vol. 80(3). link> doi>
  • Jin D, Ledger PD, Gil AJ. 2014. An hp-fem framework for the simulation of electrostrictive and magnetostrictive materials. COMPUTERS & STRUCTURES, 131-148, vol. 133. link> doi>
  • Priewald RH, Magele C, Ledger PD, Pearson NR, Mason JSD. 2013. Fast Magnetic Flux Leakage Signal Inversion for the Reconstruction of Arbitrary Defect Profiles in Steel Using Finite Elements. IEEE TRANSACTIONS ON MAGNETICS, 506-516, vol. 49(1). link> doi>
  • Gil AJ and Ledger PD. 2012. A coupled hp-finite element scheme for the solution of two-dimensional electrostrictive materials. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1158-1183, vol. 91(11). link> doi>
  • Ledger PD. 2012. hp-Finite element discretisation of the electrical impedance tomography problem. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 154-176, vol. 225. link> doi>
  • Ledger PD and Zaglmayr S. 2010. hp-Finite element simulation of three-dimensional eddy current problems on multiply connected domains. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 3386-3401, vol. 199(49-52). link> doi>
  • Zolgharni M, Griffiths H, Ledger PD. 2010. Frequency-difference MIT imaging of cerebral haemorrhage with a hemispherical coil array: numerical modelling. Physiol Meas, S111-S125, vol. 31(8). link> doi>
  • Griffiths H, Zolgharni M, Ledger PD, Watson S. 2010. The cardiff Mk2b MIT head array: Optimising the coil configuration. Journal of Physics: Conference Series, Article 012046, vol. 224. doi> link>
  • Zolgharni M, Ledger PD, Griffiths H. 2009. Forward modelling of magnetic induction tomography: a sensitivity study for detecting haemorrhagic cerebral stroke. Med Biol Eng Comput, 1301-1313, vol. 47(12). link> doi>
  • Zolgharni M, Ledger PD, Armitage DW, Holder DS, Griffiths H. 2009. Imaging cerebral haemorrhage with magnetic induction tomography: numerical modelling. Physiol Meas, S187-S200, vol. 30(6). link> doi>
  • Ledger PD. 2009. Preconditioners for the indefinite linear system arising from the hp discretization of Maxwell's equations. COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, 275-289, vol. 25(3). link> doi>
  • Ledger PD. 2007. Preconditioners for solving the indefinite linear system for higher order H (curl) discretisations. PAMM, 2130007-2130008, vol. 7(1). doi>
  • Ledger PD and Morgan K. 2005. The application of the hp-finite element method to electromagnetic problems. ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING, 235-302, vol. 12(3). link> doi>
  • Hiptmair R and Ledger PD. 2005. Computation of resonant modes for axisymmetric Maxwell cavities using hp-version edge finite elements. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1652-1676, vol. 62(12). link> doi>
  • Ledger PD, Peraire J, Morgan K, Hassan O, Weatherill NP. 2004. Parameterised electromagnetic scattering solutions for a range of incident wave angles. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 3587-3605, vol. 193(33-35). link> doi>
  • Ledger PD, Peraire J, Morgan K, Hassan O, Weatherill NP. 2003. Adaptive hp finite element computations of the scattering width output of Maxwell's equations. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 953-978, vol. 43(8). link> doi>
  • Ainsworth M, Coyle J, Ledger PD, Morgan K. 2003. Computing Maxwell eigenvalues by using higher order edge elements in three dimensions. IEEE TRANSACTIONS ON MAGNETICS, 2149-2153, vol. 39(5). link> doi>
  • Ledger PD, Morgan K, Hassan O, Weatherill NP. 2003. Plane wave H(curl; Omega) conforming finite elements for Maxwell's equations. COMPUTATIONAL MECHANICS, 272-283, vol. 31(3-4). link> doi>
  • Ledger PD, Morgan K, Peraire J, Hassan O, Weatherill NP. 2003. The development of an hp-adaptive finite element procedure for electromagnetic scattering problems. FINITE ELEMENTS IN ANALYSIS AND DESIGN, 751-764, vol. 39(8). link> doi>
  • Ledger PD, Morgan K, Hassan O, Weatherill NP. 2002. Arbitrary order edge elements for electromagnetic scattering simulations using hybrid meshes and a PML. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 339-358, vol. 55(3). link> doi>

Other

  • Ledger PD and Lionheart WRB. 2017. Magnetic polarizability tensors for low frequency object classification and detection. 2017 International Applied Computational Electromagnetics Society Symposium - Italy (ACES). IEEE. doi>
  • Priewald RH, Ledger PD, Pearson NR, Mason JSD. 2014. Uncertainties of MFL Signal Inversion and Worst-Case Defect Depth Estimation using a Numerical Model. ELECTROMAGNETIC NONDESTRUCTIVE EVALUATION (XVI) (pp. 55-+, vol. 38). link> doi>
  • Ledger PD. 2010. An Investigation of a Preconditioner for High-Frequency Maxwell Problems. ELECTROMAGNETICS (pp. 94-126, vol. 30). link> doi>
  • Ledger PD and Morgan K. 2008. An adjoint enhanced reduced-order model for monostatic RCS computation. ELECTROMAGNETICS (pp. 54-76, vol. 28). link> doi>
  • Ledger PD, Morgan K, Hassan O. 2007. Electromagnetic scattering simulation using an H(curl) conforming hp finite element method in three dimensions. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS (pp. 1267-1296, vol. 53). link> doi>
  • Coyle J and Ledger PD. 2005. Evidence of exponential convergence in the computation of Maxwell eigenvalues. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (pp. 587-604, vol. 194). link> doi>
  • Ledger PD, Morgan K, Hassan O. 2005. Frequency and time domain electromagnetic scattering simulations employing higher order edge elements. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (pp. 105-125, vol. 194). link> doi>
  • Morgan K, Ledger PD, Peraire J, Hassan O, Weatherill NP. 2002. Finite element methods for electromagnetic scattering. ENGINEERING COMPUTATIONAL TECHNOLOGY (pp. 105-120). link>

Research Themes

Computational Mathematics/Computational Mechanics

Athena Swan