College of Engineering

Swansea University

Bay Campus

Fabian Way

Swansea

SA1 8EN

Tel: +44 (1792) 602554

Email:

p.d.ledger@

swansea.ac.uk

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- Dr Paul Ledger

Specialist Subjects: Hp Finite Elements, Computational Electromagnetics, Error estimation, Reduced Order Modelling, Efficient Preconditioning, Inverse problems.

- PhD Civil and Computational Engineering, Swansea University, 2001

Thesis: An hp adaptive finite element procedure for electromagnetic scattering problems - MSc Computer modelling with finite elements, Swansea University, 1999

Thesis: Edge elements for waveguide and scattering problems - BEng Civil Engineering with Computational Mechanics, Birmingham University 1998

Thesis: The boundary element solution of water wave problems

Programming and development of H(curl) conforming finite element software capable of hp refinement in two and three dimensions.

Further interests in to the development of preconditioners for indefinite linear systems, inverse problems, uncertainty quantification, a-posteriori error estimation schemes, goal orientated adaptivity, reduced order modelling and novel schemes for reducing dispersion in wave propagation problems.

Applications to problems in computational electromagnetics, including scattering computation, eddy current computation, eigenvalue computation and more recently the modelling of biomedical imaging devices.

For further details see:

- P.D. Ledger and W.R.B. Lionheart Understanding the magnetic polarizability tensor,
*IEEE Transactions on Magnetics*, 2016 In Print: doi: 10.1109/tmag.2015.2507169. - D. Jin, P.D. Ledger and A.J. Gil. hp-Finite element solution of coupled stationary magnetohydrodynamics problems including magnetostrictive effects.
*Computers & Structures*, 2016;**164**: 161-180. - P.D. Ledger, A.J. Gil, R. Poya and S. Bagwell. Solution of an industriallly relevent coupled magneto-mechanical problem set on an axisymmetric domain.
*Applied Mathematical Modelling,*2016;**40**: 1959-1971. - P.D. Ledger and W.R.B. Lionheart, Characterising the shape and material properties of hidden targets from magentic induction data.
*IMA Journal of Applied Mathematics*, 2015;**80**: 1776-1798. - P.D. Ledger and W.R.B. Lionheart, The perturbation of electromagnetic fields at distances that are large compared with the object's size.
*IMA Journal of Applied Mathematics,*2015;**80**: 865-892. - R. Poya, A.J. Gil and P.D. Ledger, A computational framework for the analysis of linear piezoelectric beams using hp-FEM,
*Computers & Structures,*2015;**152:**155-172. - D. Jin, P.D. Ledger and A.J. Gil, An hp framework for the simulation of electro/magnetostrictive materials,
*Computers & Structures*, 2014;**133**: 131-148. - R. Priewald, C. Magele, P.D. Ledger, N.R. Pearson and J.S.D. Mason, Fast magnetic flux leakage inversion for the reconstruction of arbitary defect profiles in steel using finite elements.
*IEEE Transactions on Magnetics,*2013;**49:**506-516. - A.J. Gil and P.D. Ledger. A coupled
*hp*finite element scheme for the solution of two dimensional electrostriction materials.*International Journal for Numerical Methods in Engineering,*2012;**91**: 1158-1183. - P.D. Ledger.
*hp*-Finite element discretisation of the electrical impedance tomography problem,*Computer Methods in Applied Mechanics and Engineering*, 2012;**225-228**: 154-176. - P.D. Ledger and S. Zaglmayr.
*hp*-Finite element simulation of three-dimensional eddy current problems on multiply connected domains.*Computer Methods in Applied Mechanics and Engineering*, 2010;**199**: 3386-3401. - P.D. Ledger. An investigation of a preconditioner for high frequency Maxwell problems.
*Electromagnetics,*2010;**30:**94-126. - M. Zolgharni, P.D. Ledger and H. Griffiths. Frequency difference MIT imaging of cerebral haemorrhage with a hemispherical coil array: numerical modelling,
*Physiological Measurement*, 2010;**31**: 111-125. - M. Zolgharni, P.D. Ledger and H. Griffiths. Forward modelling for magnetic induction tomography for cerebral stroke.
*Medical & Biological Engineering & Computing*, 2009;**47**: 1301-1313. - M. Zolgharni, P.D. Ledger, D.W. Armitage, H. Griffiths and D.S. Holder. Imaging cerebral haemorrhage with magnetic impedance tomography: numerical modelling,
*Physiological Measurement*, 2009;**30**: 187-200. - P.D. Ledger. Preconditioners for the indefinite linear system arising from
*hp*discretisation of Maxwell's equations.*Communications in Numerical Methods in Engineering,*2009;**25**: 275-289. - P.D. Ledger and K. Morgan. An adjoint enhanced reduced order model for monostatic RCS computation.
*Electromagnetics*2008;**28**: 54-76. - P.D. Ledger, K. Morgan and O. Hassan. Electromagnetic scattering simulation using an H(curl) conforming
*hp*finite element method in three dimensions.*International Journal for Numerical Methods in Fluids*2007;**53**: 1267-1296. - P.D. Ledger and K. Morgan. The application of the
*hp*finite element method to electromagnetic problems.*Archives of Computational Methods in Engineering*2005;**12**: 235-302. - R. Hiptmair and P.D. Ledger. Computation of resonant modes for axisymmetric cavities using
*hp*version finite elements.*International Journal for Numerical Methods in Engineering*2005;**62**: 1652-1676. - P.D. Ledger, K. Morgan and O. Hassan. Frequency and time domain electromagnetic scattering simulations employing higher order edge elements.
*Computer Methods in Applied Mechanics and Engineering*2005;**194**: 105-125. - P.D. Ledger and J. Coyle. Evidence of exponential convergence in computing Maxwell eigenvalues.
*Computer Methods in Applied Mechanics and Engineering*2005;**194**: 587-604. - P.D. Ledger J. Peraire, K. Morgan, O. Hassan and N.P. Weatherill. Parametrised electromagnetic scattering solutions for a range of incident wave angles.
*Computer Methods in Applied Mechanics and Engineering*, 2004;**193**: 3587-3605. - M. Ainsworth, J Coyle, P.D. Ledger and K. Morgan. Computation of Maxwell eigenvalues using higher order edge elements in three dimensions.
*IEEE Transactions on Magnetics*, 2003;**39**: 2149-2153. - P.D. Ledger, K. Morgan, J. Peraire, O. Hassan and N.P. Weatherill. The development of an
*hp*-adaptive finite element procedure for electromagnetic scattering problems.*Finite Element Analysis and Design*, 2003;**39**: 751-764. - P.D. Ledger, K. Morgan, O. Hassan and N.P. Weatherill. Plane wave H(curl) conforming finite elements for Maxwell's equations.
*Computational Mechanics*, 2003;**31**: 272-283. - P.D. Ledger, J. Peraire, K. Morgan, O. Hassan and N.P. Weatherill. Adaptive
*hp-*finite element computations of the scattering width output of Maxwell's equations.*International Journal of Numerical Methods in Fluids*, 2003;**43**: 953-978. - P.D. Ledger, K. Morgan, O. Hassan and N.P. Weatherill. Arbitrary order edge elements for electromagnetic scattering problems using hybrid meshes and a PML.
*International Journal of Numerical Methods in Engineering*, 2002;**55**: 339--358.

- EG-396 - Computational Aerodynamics (15/16)
- EG-190 - Engineering Analysis 2 (15/16)
- EG-189 - Engineering Analysis 1 (15/16)

- 2014 - Simulation of magneto-mechanical coupling for MRI Scanners (2nd Supervisor: Dr Antonio Gil)
- 2011 - 'An hp-finite element Computational Framework for Nonlinear Magneto-Fluid Problems including Magnetostriction' (2nd Supervisor: Dr Antonio Gil)
- 2009 - 'Characterisation of Defects in Steel Plates from MFL Signals using Inverse Finite Element Modelling' (1st Supervisor: Dr John Mason)
- 2008 - Magnetic induction tomography for imaging cerebral stroke (1st Supervisor: Professor Huw Griffiths)

- 2011 - Computational simulation of magneto-mechanical effects (1st Supervisor: Dr Antonio Gil)
- 2008 - Magnetic induction tomography for imaging cerebral stroke (1st Supervisor: Professor Huw Griffiths)

- 2011 - To be defined
- 2010 - 'Error Estimation and Adaptivity in Engineering Simulation'
- 2009 - Coupled Finite Element Simulation of Electrostrictive Fluids (2nd Supervisor: Dr Antonio Gil)
- 2008 - Simulaton of coupled Electrostatic mechanical behavior with the finite element method (1st Supervisor: Dr Antonio Gil)

- Describing metal detection signals using polarizabiity tensors, Mathematics Colloquim, The University of Reading, March 2016
- Describing the response from metallic targets using polarizability targets, Applied Mathematics Seminars, The University of Greenwich, November 2015
- Describing the response from metallic targets using polarizability targets, British Applied Mathematics Colloquim, The University of Cambridge, April 2015.
- High order hp-finite elements in electromagnetisim and coupled problems, Association of Computational Mechanics in Engineering (UK), Swansea University, April 2015.
- Characterising the shape and material properties of hidden targets from magnetic induction data, Applied Mathematics Colloquim, Cardiff University, February 2014.
- Characterising the shape and material properties of hidden targets from magnetic induction data, Inverse Problems Seminar Series, The University of Manchester, December 2013.
- Application of hp finite elements to the accurate computation of polarisation tensors for the eddy current problem, Applied Inverse Problems Conference, Daejeon South Korea, July 2013.
- Application of hp finite elements to the accurate computation of polarisation tensors for the eddy current problem, MAFELAP Conference, Brunel University, June 2013.
- An application of hp adaptivity to electrical impedance tomography and some application of hp-FEM to coupled problems, ECCOMAS Congress, Vienna, Austria 2012.
- Application of high order finite elements to the electrical impedance tomography (EIT) inverse problem, AT-CEM, Glasgow 2011.
- An hp finite element approach to electro-mechanical problems: electrostriction, ECCM Conference, Paris, France, 2010.
- Eddy current simulations: Medical applications and efficient computation, Graz University of Technology, Austria, September 2009.
- Efficient preconditioning for high order edge elements applied to wave propagation and eddy current problems, MAFELAP Conference, Brunel University, June 2009.
- Eddy current simulations: Medical applications and efficient computation, Fallstuduim ETH Zurich, Switzerland, April 2009.
- Higher order finite elements for electromagnetics, Department of Mathematics Colloquium, University of Reading, UK, March 2009.
- Finite elements in electromagnetics: subtleties in discretisation. Computer Science Colloquium, Cardiff University, UK, February 2009.
- Higher order finite elements in electromagnetics, Applied/Computational Mathematics Colloquium, Graz University of Technology, Graz, Austria, August 2008.
- A preconditioner for indefinite linear systems arising from H(curl) discretisations, The 9th International Workshop on Finite Elements for Microwave Engineering, Bonn, Germany, May 2008.
- Adjoint enhanced reduced order model for rapid computation of outputs of interest, The 9th International Workshop on Finite Elements for Microwave Engineering, Bonn, Germany, May 2008.
- Finite elements in electromagnetics: subtlties in discretisation, Applied Mathematics Colloquium, Johannes Kepler University, Linz, Austria, December 2007.
- A comparison of solution techniques for linear systems for H(curl) problems, US National Congress on Computational Mechanics, July 2007.
- Recent developments in hp finite elements for problems in electromagnetics. School of Mathematics Colloquium, University of Nottingham, February 2007.
- Recipes for overcoming the numerical dispersion associated with finite element discretisation of electromagnetic scattering problems. Dept. Mathematics Colloquium, University of Basel, December 2004.
- Calculation of Maxwell eigenvalues using H(curl) conforming hp version finite element method. ICOSAHOM, Brown University, June 2004

Computation of Maxwell eigenvalues with exponential rates of convergence. Olberwolfach meeting on Computational Electromagnetics. February 2004. - An hp adaptive procedure for electromagnetic scattering problems. ECCOMAS PhD award presentation. ADMOS Conference Götenburg Sweden, October 2003
- Three dimensional Maxwell eigenvalue computations employing higher order edge elements. MAFELAP, Brunel University June 2003.

- Winner of the 2002 ECCOMAS PhD award for the best PhD thesis in 2002 on Computational Methods in Applied Science and Engineering awarded in Sweden, October 2003.
- Winner of the 2002 ACME Phd award for the best UK PhD thesis in 2002 on Computational Mechanics.
- Finalist for the 2002 Melosh Medal.
- Awarded fellowship to attend the first M.I.T. Conference on Fluid and Solid Mechanics, June 2001.
- Winner of the Tom Essay Prize in water engineering from the University of Birmingham, July 1998.
- Winner of the Whittaker Ellis Bullock Prize from the University of Birmingham, July 1996.

*EPSRC Small Mathematics Grant on Maxwell Generalised Polarisation Tensors. July 2013-July 2015*, Joint with Professor Lionheart, University of Manchester (£27K).*EPSRC Project on Inverse Maxwell Problems for Magnetic Induction Tomography. September**2013- September 2016*, Joint with Professors Brown, Marletta and Walker, Cardiff University (£240K (Swansea), £500K (Cardiff)).*EPSRC Bridging the Gaps Project on coupled electro-mechanical simulations using hp-FEM for Geophysical Applications.*March 2012. (£3K).*HESTEM project funding Swansea University's College of Engineering Mathematics Support Service in 2011-2012*. July 2011. (£7K).*Swansea University small teaching grant for the use of Tablet PC's in engineering mathematics lectures*. August 2011. (£500).*Royal Society travel grant (France).*November 2009. (£1.5K).*Royal Society travel grant (Austria).*February 2008. (£1K).*Royal Academy of Engineering conference grant (Germany).*March 2008. (£300).*Royal Society conference grant (US).*December 2006. (£1.1K).

I've set up and run a Mathematics Cafe since 2011 where students can go to get help with the mathematical topics of their engineering degree. Intiail support was provided by HESTEM and has been supported by the College of Engineering since 2012. To find out more see

Engineering Mathematics Resources and Cafe

I'm also the leader of the Engineering Mathematics Subject Teaching panel where I coordinate the deliver of the engineering mathematics modules to our first undergrauate students. In recent years I've taken an active role in the implementation of e-learning and e-assesment of engineering mathematics to large cohorts of students.