**Associate Professor**

Department of Mathematics

University College London

Gower Street

London

WC1E 6BT

United Kingdom

E-mail: d.hewett@ucl.ac.uk

Web: https://www.ucl.ac.uk/~ucahdhe/

Tel: +44 (0)20 7679 9229, Ext: 09229

Room: 4.12

I am an Associate Professor in the Department of Mathematics at University College London and an OCIAM Visiting Fellow in the Oxford Mathematical Institute.

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.
- Homogenized boundary conditions for scattering by periodic interfaces, for instance in electromagnetic shielding by Faraday cages.
- Scattering by fractal screens and apertures.
- Function spaces on rough domains.

- Recent grant success: "Rhythms of fractals and collective movement" - UCL Culture/EPSRC Impact Acceleration Account award with Angelika Manhart (UCL maths) and Bernhard Schimpelsberger (freelance musician) to investigate connections between our mathematical research and musical rhythms (Jan-Jul 2020)

- J. Bannister, A. Gibbs, D. P. Hewett,
**Acoustic scattering by impedance screens/cracks with fractal boundary: well-posedness analysis and boundary element approximation**, under review, 2020. preprint - A. Kleanthous, T. Betcke, D. P. Hewett, P. Escapil-Inchauspé, C. Jerez-Hanckes, A. J. Baran,
**Accelerated Calderón preconditioning for Maxwell transmission problems**, under review, 2020. preprint

- A. 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - S. N. Chandler-Wilde, D. P. Hewett, A. Moiola,
**Sobolev spaces on non-Lipschitz subsets of R**^{n}**with application to boundary integral equations on fractal screens**, Integr. Equat. Operat. Th., 87(2), 179-224, 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), 731-770, 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 numerical-asymptotic methods for high frequency scattering**, Euro. J. Appl. Math., 26(5), 773-793, 2015 article preprint - S. J. Chapman, D. P. Hewett, L. N. Trefethen,
**Mathematics of the Faraday cage**, SIAM Review, 57(3), 398-417, 2015 article preprint - 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 - D. P. Hewett,
**Tangent ray diffraction and the Pekeris caret function**, Wave Motion, 57, 257-267, 2015 article preprint - 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 - 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* - 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 - 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 - 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 - 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*** - 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 - D. P. Hewett,
**High frequency sound propagation in a network of interconnecting streets**, J. Sound Vib., 331(25), 5537-5561, 2012 article preprint - 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

- 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^{nd}International 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^{th}International Conference on Theoretical and Computational Acoustics (ICTCA), Dresden, 2009, Stefan Marburg ed., pp. 161-170, preprint

- 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

**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), 633-639 (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

- "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-Jul 2020)
- "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

- 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)

- Minisymposium on "Advances in Integral Equations" at MAFELAP 2019 (June 2019, London)
- Minisymposium on "New applications and advances in the analysis of wave scattering" at BAMC 2019 (April 2019, Bath)
- Wave propagation in complex domains (30 March 2017, London)
- Minisymposium on "Wave-based discretizations" at WAVES 2015 (July 2015, Karlsruhe)
- Scattering, Clouds and Climate: A Short Workshop of Exploration (March 2014, Oxford)
- Mathmondes 2012 (July 2012, Reading)

I am an Associate Editor for the IMA Journal of Applied Mathematics

I take a keen interest in the personal and professional development of young researchers. I have delivered training on a number of Oxford MPLS Division 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):

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

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.

Born 1982 in Chertsey, UK

Secondary education at The Romsey School, Romsey, Hampshire

Sixth-form education at Peter Symonds College, Winchester, Hampshire

MMath, University of Warwick (2002-2006)

DPhil, OCIAM, University of Oxford (2006-2010)

Postdoctoral Research Fellow, University of Reading (2010-2013)

Hooke Research Fellow, University of Oxford (2013-2016)

Lecturer in Applied Mathematics, University College London (2016-)