David Hewett
Professor of Mathematics
Department of Mathematics
University College London
25 Gordon Street
London
WC1H 0AY
United Kingdom
Email: d.hewett@ucl.ac.uk
Web: https://www.ucl.ac.uk/~ucahdhe/
Room: 4.12
About me
I am a Professor of Mathematics in the Department of Mathematics at University College London and an OCIAM Visiting Fellow in the Oxford Mathematical Institute.
Research interests
My research concerns the mathematical study of wave propagation and its applications.
My research is at the interfaces between rigorous applied and numerical analysis, asymptotic analysis and mathematical modelling.
My interests include:
 Boundary integral equations and boundary element methods
 High frequency scattering, both the study of canonical problems in geometrical optics and the geometrical theory of diffraction, and the hybridization of these asymptotic methods with numerical boundary element approximations
 Scattering by fractals
 Function spaces on rough domains
 Numerical quadrature for singular and oscillatory integrals
 Applications in atmospheric physics and urban acoustics
 Homogenized boundary conditions for scattering by periodic interfaces, for instance in electromagnetic shielding by Faraday cages
Maths and music
Youtube video (approx 4 mins long) about my collaboration
"Rhythms of fractals and collective movement" with Angelika Manhart (mathematical biologist, formerly at UCL, now at University of Vienna) and Bernhard Schimpelsberger (percussionist) on the connections between our mathematical research and musical rhythms
Publications
Journal articles under review
 A. M. Caetano, S. N. ChandlerWilde, X. Claeys, A. Gibbs, D. P. Hewett, A. Moiola, Integral equation methods for acoustic scattering by fractals.
preprint
Refereed journal articles
 A. M. Caetano, S. N. ChandlerWilde, A. Gibbs, D. P. Hewett, A. Moiola, A Hausdorffmeasure boundary element method for acoustic scattering by fractal screens, Numer. Math., 156, 463–532, 2024. article (open access)
preprint
 A. Gibbs, D. P. Hewett, D. Huybrechs, Numerical evaluation of oscillatory integrals via automated steepest descent contour deformation, J. Comp. Phys., 501, 112787, 2024.
article (open access)
preprint

J. R. Ockendon, H. Ockendon, R. H. Tew, D. P. Hewett, A. Gibbs, A caustic terminating at an inflection point, Wave Motion, 125, 103257, 2024. article (open access)
preprint
 A. Gibbs, D. P. Hewett, B. Major, Numerical evaluation of singular integrals on nondisjoint selfsimilar fractal sets, Numer. Alg., published online 15 Dec 2023. article (open access) preprint

A. Kleanthous, A. J. Baran, T. Betcke, D. P. Hewett, C. D. Westbrook, An application of the boundary element method (BEM) to the calculation of the singlescattering properties of very complex ice crystals in the microwave and submillimetre regions of the electromagnetic spectrum, J. Quant. Spectrosc. Ra., 312, 108793, 2024. article
 A. Gibbs, D. P. Hewett, A. Moiola, Numerical quadrature for singular integrals on fractals, Numer. Alg., 92, 20712124, 2023. article (open access) preprint
 A. Kleanthous, T. Betcke, D. P. Hewett, P. EscapilInchauspé, C. JerezHanckes, A. J. Baran, Accelerated Calderón preconditioning for Maxwell transmission problems, J. Comp. Phys, 458, 111099, 2022. article (open access) preprint
 J. Bannister, A. Gibbs, D. P. Hewett, Acoustic scattering by impedance screens/cracks with fractal boundary: wellposedness analysis and boundary element approximation, Math. Mod. Meth. Appl. Sci. (M3AS), 32(2), 291319, 2022.
article preprint
 A. M. Caetano, D. P. Hewett, A. Moiola, Density results for Sobolev, Besov and TriebelLizorkin spaces on rough sets, J. Funct. Anal., 281(3), 109019, 2021. article preprint
 S. N. ChandlerWilde, D. P. Hewett, A. Moiola, J. Besson, Boundary element methods for acoustic scattering by fractal screens, Numer. Math., 147(4), 785837, 2021. article (open access) preprint
 A. Gibbs, D. P. Hewett, D. Huybrechs, E. Parolin, Fast hybrid numericalasymptotic boundary element methods for high frequency screen and aperture problems based on leastsquares collocation, SN Partial Differ. Equat. Appl., 1(21), 2020. article (open access) preprint
 B. Delourme, D. P. Hewett, Electromagnetic shielding by thin periodic structures and the Faraday cage effect, C. R. Acad. Sci. I  Math, 358 (7), 777784, 2020. article preprint
 A. Kleanthous, T. Betcke, D. P. Hewett, M. Scroggs, A. J. Baran, Calderón preconditioning of PMCHWT boundary integral equations for scattering by multiple absorbing dielectric particles, J. Quant. Spectrosc. Ra., 224, 383395, 2019. article preprint
 D. P. Hewett, J. R. Ockendon, V. P. Smyshlyaev, Contour integral solutions of the parabolic wave equation, Wave Motion, 84, 90109, 2019. article preprint
 S. P. Groth, D. P. Hewett, S. Langdon, A high frequency boundary element method for scattering by penetrable convex polygons, Wave Motion, 78, 3253, 2018. article preprint
 S. N. ChandlerWilde, D. P. Hewett, Wellposed PDE and integral equation formulations for scattering by fractal screens, SIAM J. Math. Anal., 50(1), 677717, 2018. article preprint
 D. P. Hewett, A. Moiola, A note on properties of the restriction operator on Sobolev spaces, J. Appl. Anal., 23(1), 18, 2017. article preprint
 S. N. ChandlerWilde, D. P. Hewett, A. Moiola, Sobolev spaces on nonLipschitz subsets of R^{n} with application to boundary integral equations on fractal screens, Integr. Equat. Operat. Th., 87(2), 179224, 2017. article preprint
 D. P. Hewett, A. Moiola, On the maximal Sobolev regularity of distributions supported by subsets of Euclidean space, Anal. Appl., 15(5), 731770, 2017. article preprint
 D. P. Hewett, I. J. Hewitt, Homogenized boundary conditions and resonance effects in Faraday cages, Proc. Roy. Soc. A, 472, 2189, 2016 article preprint erratum
 D. P. Hewett, Shadow boundary effects in hybrid numericalasymptotic methods for high frequency scattering, Euro. J. Appl. Math., 26(5), 773793, 2015 article preprint
 S. J. Chapman, D. P. Hewett, L. N. Trefethen, Mathematics of the Faraday cage, SIAM Review, 57(3), 398417, 2015 article preprint
 D. P. Hewett, S. Langdon, S. N. ChandlerWilde, A frequencyindependent boundary element method for scattering by twodimensional screens and apertures, IMA J. Numer. Anal., 35 (4), 16981728, 2015 article preprint
 D. P. Hewett, Tangent ray diffraction and the Pekeris caret function, Wave Motion, 57, 257267, 2015 article preprint
 S. N. ChandlerWilde, D. P. Hewett, Wavenumberexplicit continuity and coercivity estimates in acoustic scattering by planar screens, Integr. Equat. Operat. Th., 82(3), 423449, 2015 article preprint
 D. P. Hewett, A. Morris, Diffraction by a rightangled impedance wedge: an edge source formulation, J. Acoust. Soc. Am., 137(2), 633639, 2015 article*
 S. N. ChandlerWilde, D. P. Hewett, A. Moiola, Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples, Mathematika, 61(2), 414443, 2015 article preprint CORRIGENDUM
 S. N. ChandlerWilde, D. P. Hewett, S. Langdon, A. Twigger, A high frequency boundary element method for scattering by a class of nonconvex obstacles, Numer. Math., 129(4), 647689, 2015 article preprint
 S. P. Groth, D. P. Hewett, S. Langdon, Hybrid numericalasymptotic approximation for high frequency scattering by penetrable convex polygons, IMA J. Appl. Math., 80(2), 324353, 2015 article preprint
 D. P. Hewett, U. P. Svensson, The diffracted field near the edge of a thin screen, J. Acoust. Soc. Am., 134(6), 43034306, 2013 article* erratum***
 D. P. Hewett, S. Langdon, J. M. Melenk, A high frequency hp boundary element method for scattering by convex polygons, SIAM J. Numer. Anal., 51(1), 629653, 2013 article preprint
 D. P. Hewett, High frequency sound propagation in a network of interconnecting streets, J. Sound Vib., 331(25), 55375561, 2012 article preprint
 D. P. Hewett, J. R. Ockendon, D. J. Allwright, Switching on a twodimensional scalar wave in the presence of a diffracting edge, Wave Motion, 48, 197213, 2011 article preprint
Refereed conference proceedings
 J. Bannister, A. Gibbs, D. P. Hewett, Volume integral equations on fractal domains and the Koch snowflake transmission problem, Proceedings of Waves 2022, Paris, France, July 2022 preprint
 D. P. Hewett, V. P. Smyshlyaev, The inflection point problem  from modal to scattering behaviour, Proceedings of Waves 2022, Paris, France, July 2022 preprint
 A. M. Caetano, S. N. ChandlerWilde, A. Gibbs, D. P. Hewett, A. Moiola, A Hausdorffmeasure boundary element method for scattering by fractal screens. I: Numerical analysis, Proceedings of Waves 2022, Paris, France, July 2022 preprint
 A. M. Caetano, S. N. ChandlerWilde, A. Gibbs, D. P. Hewett, A. Moiola, A Hausdorffmeasure boundary element method for scattering by fractal screens. II: Numerical quadrature, Proceedings of Waves 2022, Paris, France, July 2022 preprint
 J. Bannister, D. P. Hewett, Acoustic scattering by impedance screens with fractal boundary, Proceedings of Waves 2019, Vienna, Austria, July 2019 preprint
 A. Gibbs, D. P. Hewett, D. Huybrechs, E. Parolin, Least squares collocation for a highfrequency scattering problem, Proceedings of Waves 2019, Vienna, Austria, July 2019 preprint
 B. Delourme, D. P. Hewett, Electromagnetic shielding by thin periodic structures and the Faraday cage effect, Proceedings of Waves 2019, Vienna, Austria, July 2019 preprint
 A. Kleanthous, T. Betcke, D. P. Hewett, C. JerezHanckes, P. EscapilInchauspé, A. J. Baran, Fast Calderón preconditioning of the PCMHWT formulation for scattering by multiple dielectric particles, Proceedings of Waves 2019, Vienna, Austria, July 2019 preprint
 S. N. ChandlerWilde, D. P. Hewett, A. Moiola, Boundary element methods for scattering by fractal screens, Proceedings of Waves 2019, Vienna, Austria, July 2019 preprint
 D. P. Hewett, I. J. Hewitt, Faraday cages: homogenized boundary conditions and resonance effects, Proceedings of Waves 2017, Minneapolis, USA, May 2017 preprint
 J. A. Hargreaves, Y. W. Lam, S. Langdon, D. P. Hewett, A highfrequency BEM for 3D acoustic scattering, Proceedings of the 22^{nd}International Congress on Sound and Vibration, Florence, Italy, July 2015 preprint
 S. N. ChandlerWilde, D. P. Hewett, A. Moiola, Function spaces for integral equations on fractal domains, Proceedings of Waves 2015, Karlsruhe, Germany, pp. 7374 preprint
 S. P. Groth, D. P. Hewett, S. Langdon, A highfrequency boundary element method for a transmission scattering problem, Proceedings of Waves 2015, Karlsruhe, Germany, pp. 132133 preprint
 J. A. Hargreaves, D. P. Hewett, Y. W. Lam, S. Langdon,A high frequency boundary element method for scattering by threedimensional screens, Proceedings of Waves 2015, Karlsruhe, Germany, pp. 202203 preprint
 D. P. Hewett, Hybrid numericalasymptotic boundary element methods for high frequency wave scattering, Mathematisches Forschungsintitut Oberwolfach workshop 1503: "New Discretization Methods for the Numerical Approximation of PDEs", January 2015 preprint
 D. P. Hewett, S. N. ChandlerWilde, Wavenumberexplicit coercivity estimates in scattering by screens, Proceedings of Waves 2013, Gammarth, Tunisia, pp. 253254 preprint
 S. N. ChandlerWilde, D. P. Hewett, S. Langdon, A. Twigger, A high frequency hpboundary element method for scattering by twodimensional screens, Proceedings of Waves 2013, Gammarth, Tunisia, pp. 321322, preprint
 S. P. Groth, D. P. Hewett, S. Langdon, Hybrid numericalasymptotic approximation of high frequency scattering by penetrable convex polygons, Proceedings of Waves 2013, Gammarth, Tunisia, pp. 327328, preprint
 S. N. ChandlerWilde, D. P. Hewett, S. Langdon, A. Twigger, A high frequency BEM for scattering by nonconvex obstacles, Proceedings of Waves 2011, Vancouver, Nilima Nigam ed., pp. 307310 preprint
 D. P. Hewett, J. R. Ockendon, D. J. Allwright, Switching on the Sommerfeld diffraction problem, Proceedings of Waves 2011, Vancouver, Nilima Nigam ed., pp. 641644 preprint
 D. P. Hewett, Localisation of an impulsive acoustic source in an urban environment, Proceedings of the 9^{th}International Conference on Theoretical and Computational Acoustics (ICTCA), Dresden, 2009, Stefan Marburg ed., pp. 161170, preprint
Other publications
 S. N. ChandlerWilde, D. P. Hewett, Acoustic scattering by fractal screens: mathematical formulations and wavenumberexplicit continuity and coercivity estimates, Technical Report, 2013 report
 D. P. Hewett, Sound propagation in an urban environment, DPhil thesis, 2010 pdf
 T. Armour et al., Dynamic location of phone call clusters, Study Group Report, 64th European Study Group with Industry, HeriotWatt University, Edinburgh, 2008 (contributing author) report
 T. Gardener et al., Automatic measurement systems for Runway Visual Range, Study Group Report, 59th European Study Group with Industry, University of Nottingham, 2007 (contributing author) report
*Copyright (2013) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. This article appeared in J. Acoust. Soc. Am. 134(6), 43034306 (2013) and may be found at http://dx.doi.org/10.1121/1.4828824
**Copyright (2015) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. This article appeared in J. Acoust. Soc. Am. 137(2), 633639 (2015) and may be found at http://dx.doi.org/10.1121/1.4906265
***Copyright (2015) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. This article appeared in J. Acoust. Soc. Am. 137(3), 1605 (2015) and may be found at http://dx.doi.org/10.1121/1.4908215
Awards
 "Singular and oscillatory quadrature on nonsmooth domains"  EPSRC Standard Research Grant, with Andrew Gibbs (RCoI) EP/V053868/1 (Dec 2021  Nov 2024)
 "Rhythms of fractals and collective movement"  UCL Culture/EPSRC Impact Acceleration Account award to work with Angelika Manhart (UCL maths) and Bernhard Schimpelsberger (freelance musician) on the connections between our mathematical research and musical rhythms (Jan 2020  Jul 2021)
 "Integral equations on fractal domains: analysis and computation"  EPSRC New Investigator Award EP/S01375X/1 (Aug 2019  Jul 2021)
 "Integral equation methods for electromagnetic scattering by fractal structures"  EPSRC/UCL Future Leaders in Engineering and Physical Sciences grant (Aug 2016  Mar 2017)
 Extraordinary Junior Research Fellowship, The Queen's College Oxford, 20132016
 Hooke Research Fellowship, University of Oxford Mathematical Institute, 20132016
 IMA Prize 2006, University of Warwick
 "The UK's Most Enterprising Student 2005", National Shell STEP awards (see http://www.independent.co.uk/news/education/higher/shellstechnologyenterpriseprogrammeonebigstepforstudentkind479527.html
 IBM Student Recognition Scheme Award 2005, University of Warwick
Popular press
 SIAM News article by Nick Trefethen about our research into the Faraday cage effect (July 2016)
 Physics World article by journalist Andrew Silver announcing our SIAM Review article on the Faraday cage effect (September 2015)
Workshops/conference/minisymposium organisation
 UKAN+ Mathematical Acoustics Workshop (September 2023, UCL)
 Workshop on "Computational methods for multiple scattering" within the Isaac Newton Institute programme on the Mathematical Theory and Applications of Multiple Wave Scattering (January  June 2023, Cambridge)
 Workshop on "Numerics & Acoustics" (September 2022, Imperial College London, UK)
 Minisymposium on "Advances in Computational Boundary Integral Equations for Electromagnetics" at the Conference on Mathematics of Wave Phenomena 2022 (February 2022, Karlsruhe, Germany)
 Minisymposium on "Advances in Integral Equations" at MAFELAP 2019 (June 2019, Brunel University, London)
 Minisymposium on "New applications and advances in the analysis of wave scattering" at BAMC 2019 (April 2019, Bath)
 Wave propagation in complex domains (March 2017, UCL)
 Minisymposium on "Wavebased discretizations" at WAVES 2015 (July 2015, Karlsruhe, Germany)
 Scattering, Clouds and Climate: A Short Workshop of Exploration (March 2014, Oxford)
 Mathmondes 2012 (July 2012, Reading)
Editorial and other positions of responsibility
I am an Associate Editor for the IMA Journal of Applied Mathematics
I am a Coordinator of the Mathematical Analysis in Acoustics Special Interest Group of the EPSRC UK Acoustics Network Plus (UKAN+)
Personal and professional development training
I take a keen interest in the personal and professional development of young researchers. At UCL I regularly deliver training to PhD students, postdocs and new lecturers, covering various aspects of academic life. At Oxford I have delivered numerous PhD student training courses including "Foundations for a Successful DPhil" (a oneday course for firstyear DPhil students) and "GRAD Challenge" (a threeday course for 2^{nd}/3^{rd} year DPhil students). In collaboration with Alison Trinder from the Oxford MPLS Division I have delivered sessions in the Oxford Mathematical Institute "Fridays@4" series (click links for slides):
Professional affiliations
Former President and a founding member of the Oxford University SIAM Student Chapter
Previous positions
From 20132016 I was a Hooke Research Fellow in the Oxford Mathematical Institute and a Junior Research Fellow at The Queen's College, Oxford.
From 20102013 I was a Postdoctoral Research Fellow at the University of Reading, working in collaboration with Simon ChandlerWilde and Steve Langdon on the EPSRCfunded grant "Boundary integral equation methods for high frequency scattering problems". The aim of the project was to develop novel numerical methods for solving highfrequency scattering problems based on a detailed understanding of the asymptotic behaviour of the scattered wave in the highfrequency limit. The project also involved collaboration with Andrea Moiola, Samuel Groth and Ashley Twigger at the University of Reading, Ivan Graham and Euan Spence at the University of Bath and Valery Smyshlyaev and Timo Betcke at University College London  for further details and recent work in this area see the Project Homepage, and the comprehensive review article published a few years ago in Acta Numerica.
My DPhil studies at the University of Oxford from 20062010 with John Ockendon and David Allwright concerned the modelling of sound propagation in urban environments, with a particular emphasis on high frequency propagation, and on the study of the inverse problem of source localisation, where the location of a sound source is to be determined from measurements of the sound field at various receivers distributed through the propagation domain. My DPhil was an Industrial CASE Award with Dstl.
Biography
MMath, University of Warwick (20022006)
DPhil, OCIAM, University of Oxford (20062010)
Postdoctoral Research Fellow, University of Reading (20102013)
Hooke Research Fellow, University of Oxford (20132016)
Lecturer in Applied Mathematics, University College London (20162019)
Associate Professor in Mathematics, University College London (20192023)
Professor of Mathematics, University College London (2023)