Academic Education

Research Interests

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.

Invited Presentations

• 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.

Academic Prizes

• 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.
• 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.

Journal Publications

• P.D. Ledger hp-Adaptive finite element computations in electrical impedance tomography. Submitted 2011. PDF
• A.J. Gil and P.D. Ledger A coupled hp-finite element scheme for the solution of two-dimensional electrostrictive materials. Submitted 2011. PDF
• P.D. Ledger hp-Finite element discretisation of the electrical impedence tomography problem. Submitted 2011,  Research Report
• 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. PDF.
• P.D. Ledger. An investigation of a preconditioner for high frequency Maxwell problems. Electromagnetics, 2010:30: 94-126. PDF.
• M Zolgharni, H Griffiths and P D Ledger, Frequency-difference MIT imaging of cerebral haemorrhage with a hemispherical coil array: numerical modelling, Physiological Measurement,  2010:31; 111-125. PDF.
• R. Sevilla and P.D. Ledger.  A comparison of two PMLs for electromagnetic scattering problems in the time domain using high order DG methods, Computer Methods in Applied Mechanics and Engineering, in review 2009.
• 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. PDF.
• M. Zolgharni, P.D. Ledger, D.W. Armitage, D.S.Holder and H. Griffiths . Imaging cerebral haemorrhage with magnetic induction tomography: numerical modelling, Physiological Measurement, 2009: 30; 187-200. PDF.
• P.D. Ledger. Preconditioners for the indefinite linear system arising from the 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: 54-75.
• P.D. Ledger. Preconditioners for solving the indefinite linear system for higher order H(curl) discretisations. PAMM; 2007: 213007-213008.
• 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, 2004; 194:105-125.
• P.D. Ledger and J. Coyle. Evidence of exponential convergence in computing Maxwell eigenvalues. Computer Methods in Applied Mechanics and Engineering, 2004; 194: 587-604.
• P.D. Ledger, J. Peraire, K. Morgan, O. Hassan and N.P. Weatherill. Parameterised 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 for 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 for Numerical Methods in Engineering, 2002; 55:339-358.

Completed Student Theses

Completed Phd theses supervised by me:

• M. Zolgharni, Magnetic Induction Tomography for Imaging Cerebral Stroke, 2010 (jointly supervised with Professor Huw Griffiths, ABM University NHS Trust). PDF.