David Hewett

Professor of Mathematics
Department of Mathematics
University College London
25 Gordon Street
London
WC1H 0AY
United Kingdom

E-mail: d.hewett@ucl.ac.uk
Web: https://www.ucl.ac.uk/~ucahdhe/
Room: 4.15

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

Refereed journal articles

1. A. M. Caetano, S. N. Chandler-Wilde, X. Claeys, A. Gibbs, D. P. Hewett, A. Moiola, Integral equation methods for acoustic scattering by fractals, Proc. Roy. Soc. A, to appear. preprint
2. A. M. Caetano, S. N. Chandler-Wilde, A. Gibbs, D. P. Hewett, A. Moiola, A Hausdorff-measure boundary element method for acoustic scattering by fractal screens, Numer. Math., 156, 463–532, 2024. article (open access) preprint
3. 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
4. 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
5. A. Gibbs, D. P. Hewett, B. Major, Numerical evaluation of singular integrals on non-disjoint self-similar fractal sets, Numer. Alg., published online 15 Dec 2023. article (open access) preprint
6. 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 single-scattering properties of very complex ice crystals in the microwave and sub-millimetre regions of the electromagnetic spectrum, J. Quant. Spectrosc. Ra., 312, 108793, 2024. article
7. A. Gibbs, D. P. Hewett, A. Moiola, Numerical quadrature for singular integrals on fractals, Numer. Alg., 92, 2071-2124, 2023. article (open access) preprint
8. A. Kleanthous, T. Betcke, D. P. Hewett, P. Escapil-Inchauspé, C. Jerez-Hanckes, A. J. Baran, Accelerated Calderón preconditioning for Maxwell transmission problems, J. Comp. Phys, 458, 111099, 2022. article (open access) preprint
9. J. Bannister, A. Gibbs, D. P. Hewett, Acoustic scattering by impedance screens/cracks with fractal boundary: well-posedness analysis and boundary element approximation, Math. Mod. Meth. Appl. Sci. (M3AS), 32(2), 291-319, 2022. article preprint
10. A. M. Caetano, D. P. Hewett, A. Moiola, Density results for Sobolev, Besov and Triebel-Lizorkin spaces on rough sets, J. Funct. Anal., 281(3), 109019, 2021. article preprint
11. S. N. Chandler-Wilde, D. P. Hewett, A. Moiola, J. Besson, Boundary element methods for acoustic scattering by fractal screens, Numer. Math., 147(4), 785-837, 2021. article (open access) preprint
12. A. Gibbs, D. P. Hewett, D. Huybrechs, E. Parolin, Fast hybrid numerical-asymptotic boundary element methods for high frequency screen and aperture problems based on least-squares collocation, SN Partial Differ. Equat. Appl., 1(21), 2020. article (open access) preprint
13. B. Delourme, D. P. Hewett, Electromagnetic shielding by thin periodic structures and the Faraday cage effect, C. R. Acad. Sci. I - Math, 358 (7), 777-784, 2020. article preprint
14. 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, 383-395, 2019. article preprint
15. D. P. Hewett, J. R. Ockendon, V. P. Smyshlyaev, Contour integral solutions of the parabolic wave equation, Wave Motion, 84, 90-109, 2019. article preprint
16. S. P. Groth, D. P. Hewett, S. Langdon, A high frequency boundary element method for scattering by penetrable convex polygons, Wave Motion, 78, 32-53, 2018. article preprint
17. S. N. Chandler-Wilde, D. P. Hewett, Well-posed PDE and integral equation formulations for scattering by fractal screens, SIAM J. Math. Anal., 50(1), 677-717, 2018. article preprint
18. D. P. Hewett, A. Moiola, A note on properties of the restriction operator on Sobolev spaces, J. Appl. Anal., 23(1), 1-8, 2017. article preprint
19. S. N. Chandler-Wilde, D. P. Hewett, A. Moiola, Sobolev spaces on non-Lipschitz subsets of Rⁿ with application to boundary integral equations on fractal screens, Integr. Equat. Operat. Th., 87(2), 179-224, 2017. article preprint
20. D. P. Hewett, A. Moiola, On the maximal Sobolev regularity of distributions supported by subsets of Euclidean space, Anal. Appl., 15(5), 731-770, 2017. article preprint
21. 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
22. D. P. Hewett, Shadow boundary effects in hybrid numerical-asymptotic methods for high frequency scattering, Euro. J. Appl. Math., 26(5), 773-793, 2015 article preprint
23. S. J. Chapman, D. P. Hewett, L. N. Trefethen, Mathematics of the Faraday cage, SIAM Review, 57(3), 398-417, 2015 article preprint
24. D. P. Hewett, S. Langdon, S. N. Chandler-Wilde, A frequency-independent boundary element method for scattering by two-dimensional screens and apertures, IMA J. Numer. Anal., 35 (4), 1698-1728, 2015 article preprint
25. D. P. Hewett, Tangent ray diffraction and the Pekeris caret function, Wave Motion, 57, 257-267, 2015 article preprint
26. S. N. Chandler-Wilde, D. P. Hewett, Wavenumber-explicit continuity and coercivity estimates in acoustic scattering by planar screens, Integr. Equat. Operat. Th., 82(3), 423-449, 2015 article preprint
27. D. P. Hewett, A. Morris, Diffraction by a right-angled impedance wedge: an edge source formulation, J. Acoust. Soc. Am., 137(2), 633-639, 2015 article*
28. S. N. Chandler-Wilde, D. P. Hewett, A. Moiola, Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples, Mathematika, 61(2), 414-443, 2015 article preprint CORRIGENDUM
29. S. N. Chandler-Wilde, 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), 647-689, 2015 article preprint
30. S. P. Groth, D. P. Hewett, S. Langdon, Hybrid numerical-asymptotic approximation for high frequency scattering by penetrable convex polygons, IMA J. Appl. Math., 80(2), 324-353, 2015 article preprint
31. D. P. Hewett, U. P. Svensson, The diffracted field near the edge of a thin screen, J. Acoust. Soc. Am., 134(6), 4303-4306, 2013 article* erratum***
32. 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), 629-653, 2013 article preprint
33. D. P. Hewett, High frequency sound propagation in a network of interconnecting streets, J. Sound Vib., 331(25), 5537-5561, 2012 article preprint
34. D. P. Hewett, J. R. Ockendon, D. J. Allwright, Switching on a two-dimensional scalar wave in the presence of a diffracting edge, Wave Motion, 48, 197-213, 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. Chandler-Wilde, A. Gibbs, D. P. Hewett, A. Moiola, A Hausdorff-measure 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. Chandler-Wilde, A. Gibbs, D. P. Hewett, A. Moiola, A Hausdorff-measure 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 high-frequency 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. Jerez-Hanckes, P. Escapil-Inchauspé, 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. Chandler-Wilde, 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 high-frequency BEM for 3D acoustic scattering, Proceedings of the 22^ndInternational Congress on Sound and Vibration, Florence, Italy, July 2015 preprint
• S. N. Chandler-Wilde, D. P. Hewett, A. Moiola, Function spaces for integral equations on fractal domains, Proceedings of Waves 2015, Karlsruhe, Germany, pp. 73-74 preprint
• S. P. Groth, D. P. Hewett, S. Langdon, A high-frequency boundary element method for a transmission scattering problem, Proceedings of Waves 2015, Karlsruhe, Germany, pp. 132-133 preprint
• J. A. Hargreaves, D. P. Hewett, Y. W. Lam, S. Langdon,A high frequency boundary element method for scattering by three-dimensional screens, Proceedings of Waves 2015, Karlsruhe, Germany, pp. 202-203 preprint
• D. P. Hewett, Hybrid numerical-asymptotic 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. Chandler-Wilde, Wavenumber-explicit coercivity estimates in scattering by screens, Proceedings of Waves 2013, Gammarth, Tunisia, pp. 253-254 preprint
• S. N. Chandler-Wilde, D. P. Hewett, S. Langdon, A. Twigger, A high frequency hp-boundary element method for scattering by two-dimensional screens, Proceedings of Waves 2013, Gammarth, Tunisia, pp. 321-322, preprint
• S. P. Groth, D. P. Hewett, S. Langdon, Hybrid numerical-asymptotic approximation of high frequency scattering by penetrable convex polygons, Proceedings of Waves 2013, Gammarth, Tunisia, pp. 327-328, preprint
• S. N. Chandler-Wilde, D. P. Hewett, S. Langdon, A. Twigger, A high frequency BEM for scattering by non-convex obstacles, Proceedings of Waves 2011, Vancouver, Nilima Nigam ed., pp. 307-310 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. 641-644 preprint
• D. P. Hewett, Localisation of an impulsive acoustic source in an urban environment, Proceedings of the 9^thInternational Conference on Theoretical and Computational Acoustics (ICTCA), Dresden, 2009, Stefan Marburg ed., pp. 161-170, preprint

Other publications

• S. N. Chandler-Wilde, D. P. Hewett, Acoustic scattering by fractal screens: mathematical formulations and wavenumber-explicit 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, Heriot-Watt 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

Awards

• "Singular and oscillatory quadrature on non-smooth 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, 2013-2016
• Hooke Research Fellowship, University of Oxford Mathematical Institute, 2013-2016
• 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/shells-technology-enterprise-programme-one-big-step-for-studentkind-479527.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

• Singular and oscillatory integration: advances and applications (June 2024, UCL)
• 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 "Wave-based 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 one-day course for first-year DPhil students) and "GRAD Challenge" (a three-day 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):

• "Self-awareness and assertiveness for productive relationships"
  
• "Negotiation"

Professional affiliations

Former President and a founding member of the Oxford University SIAM Student Chapter

Previous positions

From 2013-2016 I was a Hooke Research Fellow in the Oxford Mathematical Institute and a Junior Research Fellow at The Queen's College, Oxford.

From 2010-2013 I was a Postdoctoral Research Fellow at the University of Reading, working in collaboration with Simon Chandler-Wilde and Steve Langdon on the EPSRC-funded grant "Boundary integral equation methods for high frequency scattering problems". The aim of the project was to develop novel numerical methods for solving high-frequency scattering problems based on a detailed understanding of the asymptotic behaviour of the scattered wave in the high-frequency 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 2006-2010 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