Theoretical and computational aspects of direct and inverse acoustic and electromagnetic scattering, especially rough surface scattering, scattering by fractals, and high frequency analysis and numerical methods.
Integral equations and their numerical treatment
Boundary integral equation methods
Spectral theory and random matrices and operators
Outdoor sound propagation and noise control
Current Teaching
For course information, lecture notes, problem sheets, etc, go to Blackboard.
MA4XJ Integral Equations.
Current and Recent Research Grants
EPSRC Centre for Doctoral Training in the Mathematics of Planet Earth at Imperial College London and the University of Reading. EPSRC, 2014-2022. With Dan Crisan, Colin Cotter, Axel Gandy, David Ham, Darryl Holm (Imperial College) & Beatrice Pelloni, Jochen Broecker, Sebastian Reich, Ted Shepherd, Hilary Weller (Reading).
Advanced numerical techniques for characterising obstructions in sewer pipes. EPSRC, 2010-2013. With Kirill Horoshenkov (Bradford) & Ray Kirby (Brunel).
New generation finite element methods for seismic forward modelling. NERC and Schlumberger Cambridge Research, 2010-2013. With Steve Langdon & Timo Betcke (Reading).
Boundary integral equation methods for high frequency scattering problems. EPSRC, 2009-2012. With Steve Langdon (Reading), Ivan Graham & Valery Smyshlyaev (Bath).
Scattering by unbounded surfaces. Leverhulme Trust, 2006-2007.
Wave scattering in unbounded domains: operator algebra and limit operator techniques. EU, 2005-2007. With Marko Lindner (Chemnitz).
Finite element methods for scattering by rough surfaces. EPSRC, 2003-2005. With Peter Monk (Delaware)
Developments in boundary element methods for acoustics and
electromagnetics. EPSRC, 2004-2005. With Sia Amini (Salford), Ke
Chen (Liverpool), Penny Davies (Strathclyde), & Ivan Graham
(Bath).
Singular integral equations on infinite domains with application to scattering by unbounded Lipschitz surfaces.
EPSRC Mathematics Programme, 2001-2002. With Bo Zhang (Coventry).
Royal Society funding for support of visit of Professor David Natroshvili, Georgian Technical University, Tbilisi, 2000-2001.
Innovative boundary element techniques in computational acoustics and electromagnetics.
EPSRC Computational Partial Differential
Equations Initiative, 2000-2001. With Ke Chen (Liverpool), Penny Davies (Strathclyde), Ivan Graham (Bath), & Mireille Levy (RAL).
Integral equation methods for direct and inverse scattering
by unbounded surfaces. EPSRC Computational Partial Differential
Equations Initiative, 1999-2003. Final Report on the Grant for EPSRC.
The scattering of elastic waves
by one-dimensional rough surfaces. EU Training and
Mobility of Researchers
(support of Tilo Arens),
1998-2000.
Boundary element methods in outdoor sound propagation.
Transport Research Laboratory, 1997-2001.
Simulation of the performance of
louvred barriers. Transport Research Laboratory, 1998.
Direct and inverse scattering by rough surfaces. British Council, 1997-2000.
With A Kirsch (Mathematisches Institut II, Universität Karlsruhe).
Acoustic performance of noise barriers. EPSRC, 1996-99. With D C Hothersall
& K V Horoshenkov (Bradford University).
Boundary element simulation of traffic noise propagation from shallow cuttings.
Transport Research Laboratory, 1995-96.
Integral equations on the real line with application to diffraction grating
and related problems. EPSRC, 1994-1997. With A D Rawlins & D C Hothersall
(Bradford University).
Control of road traffic noise. EPSRC, 1992-96. With D C Hothersall (Bradford
University) & K Attenborough (Open University).
Direct and inverse problems in the theory of diffraction gratings. British
Council, 1994-97.
On symmetries of the Feinberg-Zee random hopping matrix. S N Chandler-Wilde & R Hagger, 2017 in Operator Theory: Advances and Applications. Vol. 258, 51–78. Recent Trends in Operator Theory and Partial Differential Equations: the Roland Duduchava Anniversary Volume.
V. Maz’ya, D. Natroshvili, E. Shargorodsky and W.L. Wendland, editors.
Boundary integral methods in high frequency scattering.
S N Chandler-Wilde & I G Graham 2009 in Highly Oscillatory Problems, B Engquist, T Fokas, E Hairer, A Iserles, editors, Cambridge University Press, pp. 154-193.
Existence and uniqueness of solutions for acoustic scattering over infinite obstacles.
A Peplow & S N Chandler-Wilde 2008 Journal of Mathematical Analysis and Applications 345, 305-321.
A high-wavenumber boundary-element method for an acoustic scattering
problem. S N Chandler-Wilde, S Langdon, & L Ritter
2004 Philosophical Transactions of the Royal Society, Series A 362, 647-671.
The
Dirichlet metaharmonic Green's function for unbounded
regions. D Natroshvili & S N Chandler-Wilde 2003
Memoirs on Differential Equations and Mathematical
Physics30, 51-103.
Uniqueness, existence, and integral equation formulations for interface scattering problems.
D Natroshvili, T Arens, & S N Chandler-Wilde 2003
Memoirs on Differential Equations and Mathematical
Physics30, 105-146.
Integral equation
methods for scattering by infinite rough surfaces. B
Zhang & S N Chandler-Wilde 2003 Mathematical Methods in
the Applied Sciences26, 463-488.
The domain
derivative in rough surface scattering and rigorous estimates for
first order perturbation theory. S N Chandler-Wilde &
R Potthast 2002 Proceedings of the Royal Society of London,
Series A458, 2967-3001.
Solvability and spectral properties of integral equations on the
real line: I. weighted spaces of continuous functions. T
Arens, S N Chandler-Wilde, & K O Haseloh 2002 Journal of
Mathematical Analysis and Applications272, 276-302.
A
generalised collectively compact operator theory with an
application to second kind integral equations on unbounded
domains. S N Chandler-Wilde & B Zhang 2002
Journal of Integral Equations and Applications 14,
11-52.
Efficient calculation of two-dimensional periodic and waveguide acoustic Green's functions.
K V Horoshenkov & S N Chandler-Wilde 2002 Journal of the Acoustical Society of America 111, 1610-1622.
A fast
two-grid and finite section method for a class of integral
equations on the real line with application to an acoustic
scattering problem in the half-plane. S N
Chandler-Wilde, M Rahman, &, C R Ross 2002 Numerische
Mathematik93, 1-51.
An integral equation method for inverse scattering by rough surfaces.
C D Lines & S N Chandler-Wilde 2001 in Proceedings of the
Third UK Conference on
Boundary Integral Methods,
University of Brighton,
Brighton, September 2001, pp. 258-267. University of Brighton Press.
P.J. Harris (ed.)
On the stability and convergence of the finite section method for
integral equation formulations of rough surface scattering.
A Meier & S N Chandler-Wilde 2001 Mathematical
Methods in the Applied Sciences 24, 209-232.
A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces.
A Meier, T Arens, S N Chandler-Wilde, & A Kirsch 2000
Journal of Integral Equations and Applications12, 281-321.
Integral equation methods for scattering by one-dimensional rough surfaces.
T Arens, S N Chandler-Wilde, &
A Meier 2000 in Proceedings of the
5th International Conference on
Mathematical and Numerical Aspects of Wave Propagation, Santiago de Compostela,
Spain, July 2000, pp. 3-13. SIAM. A Bermúdez, D Gómez, C Hazard, P Joly, J E Roberts (eds.) (Invited plenary paper.)
Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions.
B Lin & S N Chandler-Wilde 2000
Journal of Hydroinformatics2, 255-267.
On the solvability of second kind integral equations on the real line.
S N Chandler-Wilde, B Zhang, & C R Ross 2000
Journal of Mathematical Analysis and Applications245, 28-51.
Proceedings of the Second UK Conference on Boundary Integral Methods, L C Wrobel & S N Chandler-Wilde, editors, 1999. Uxbridge: Brunel University Press.
Scattering by infinite
one-dimensional rough surfaces.
S N Chandler-Wilde, C R Ross, & B Zhang 1999
Proceedings of the Royal Society of London, Series A 455, 3767-3787.
Noise propagation from a cutting of arbitrary cross-section and impedance.
A T Peplow & S N Chandler-Wilde 1999
Journal of Sound and Vibration 223, 355-378.
The combined effects of porous asphalt surfacing and barriers on traffic noise.
G R Watts, S N Chandler-Wilde, & P A Morgan 1999 Applied Acoustics58, 351-377.
Scattering of electromagnetic waves by rough interfaces
and inhomogeneous
layers.
S N Chandler-Wilde & B Zhang 1999 SIAM Journal on Mathematical
Analysis30, 559-583.
A uniqueness result for scattering by infinite rough surfaces.
S N Chandler-Wilde & B Zhang 1998 SIAM Journal on Applied Mathematics
58, 1774-1790.
Acoustic scattering by an inhomogeneous layer on a rigid plate.
B Zhang & S N Chandler-Wilde 1998 SIAM Journal on Applied Mathematics
58, 1931-1950.
Influence of shape and absorbing surface - A numerical study of railway
noise barriers.
P A Morgan, D C Hothersall, & S N ChandlerWilde 1998 Journal
of Sound and Vibration 217, 405-417.
Padé approximants for the acoustical properties of rigid frame porous
media with pore size distributions.
K V Horoshenkov, K Attenborough, & S N ChandlerWilde 1998 Journal
of the Acoustical Society of America 104, 1198-1209.
Electromagnetic scattering by an inhomogeneous conducting or dielectric
layer on a perfectly conducting plate.
S N Chandler-Wilde & B Zhang 1998 Proceedings of the Royal Society
of London, Series A 454, 519-542.
Tyndall Medal lecture: the boundary element method in outdoor noise propagation.
S N Chandler-Wilde 1997 Proceedings of the Institute of Acoustics
19(8), 27-50.
On the solvability of a class of second kind integral equations on unbounded
domains.
S N Chandler-Wilde & B Zhang 1997 Journal of Mathematical Analysis
and Applications 214, 482-502.
The impedance boundary value problem for the Helmholtz equation in a half-plane.
S N Chandler-Wilde 1997 Mathematical Methods in the Applied Sciences
20, 813-840.
A depth-integrated 2D coastal and estuarine model with conformal boundary-fitted
mesh generation.
B Lin & S N Chandler-Wilde 1996 International Journal for Numerical
Methods in Fluids23, 819-846.
Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation
in a non-locally perturbed half-plane.
S N Chandler-Wilde & C R Ross 1996 Mathematical Methods in the
Applied Sciences 19, 959-976.
Asymptotic behavior at infinity of solutions of multidimensional second
kind integral equations.
S N Chandler-Wilde & A T Peplow 1995 Journal of Integral Equations
and Applications 7, 303-327.
Uniqueness results for direct and inverse scattering by infinite surfaces
in a lossy medium.
S N Chandler-Wilde & C R Ross 1995 Inverse Problems 10,
1063-1067.
Padé approximants for the acoustical characteristics of porous media.
S N Chandler-Wilde & K V Horoshenkov 1995 Journal of the Acoustical
Society of America 98, 1119-1129.
Approximate solution of second kind integral equations on infinite cylindrical
surfaces. A T Peplow & S N Chandler-Wilde 1995 SIAM Journal on Numerical
Analysis 32, 594-609.
Multiple-edge noise barriers. D H Crombie, D C Hothersall & S N Chandler-Wilde
1995 Applied Acoustics 44, 353-367.
Evaluation of a boundary integral formulation for the conformal mapping
of the unit disk onto a simply-connected domain. S N Chandler-Wilde, J
Levesley & D M Hough 1995 Advances in Computational Mathematics
3, 115-135.
Boundary value problems for the Helmholtz equation in a half-plane. S N
Chandler-Wilde 1995 in Proceedings of the 3rd International Conference
on Mathematical and Numerical Aspects of Wave Propagation, Mandelieu-La
Napoule, France, April 1995, pp. 188-197. SIAM.
Scattering by one-dimensional rough surfaces. S N Chandler-Wilde &
C R Ross 1995 in Proceedings of the 3rd International Conference on
Mathematical and Numerical Aspects of Wave Propagation, Mandelieu-La
Napoule, France, April 1995, pp. 208-215. SIAM.
A uniformly valid far field asymptotic expansion for the Green function
for two-dimensional propagation above a homogeneous impedance plane. S
N Chandler-Wilde & D C Hothersall 1995 Journal of Sound and Vibration
182, 665-675.
Efficient calculation of the Green function for acoustic propagation above
a homogeneous impedance plane. S N Chandler-Wilde & D C Hothersall
1995 Journal of Sound and Vibration 180, 705-724.
On asymptotic behavior at infinity and the finite section method for integral
equations on the half-line. S N Chandler-Wilde 1994 Journal of Integral
Equations and Applications 6, 37-74.
Some uniform stability and convergence results for integral equations on
the real line and projection methods for their solution. S N Chandler-Wilde
1993 IMA Journal of Numerical Analysis 13, 509-535.
Previous Research Students and Staff
Former Students
Dr David Berry, PhD awarded October 1990 from Department of
Engineering Mechanics,
The Open University. "Acoustic
scattering by near-surface inhomogeneities in a porous
half-space". (Now at University of Evora, Portugal.)
Professor Jeremy Levesley, PhD awarded July 1991 from Department of Mathematics,
Coventry Polytechnic.
"Fast integral equation methods for numerical
conformal mapping and boundary fitted mesh generation".
(Now at University of Leicester.)
Dr Andrew Peplow.
PhD awarded July 1996 from Department of Civil
Engineering,
University of Bradford. "Boundary integral equation methods
in outdoor sound propagation". EPSRC funded.
(Now at Applied Analysis and Computation Group, Imperial College London.)
Dr Chris Ross, PhD awarded July 1997 from Brunel University.
"Direct and inverse problems in rough surface scattering".
EPSRC funded. (Now at European Patent Office in Munich.)
Dr Philip Morgan, PhD awarded
November 1999 from Brunel University.
"Boundary element modelling and
full scale measurement of the acoustic performance of
outdoor noise barriers". (Click here to download thesis.) EPSRC CASE Student with Transport Research Laboratory.
(Now Senior Transport Noise Researcher at the
Transport
Research Laboratory.)
Dr Tilo Arens,
PhD awarded June 2000 from Brunel University.
"Scattering of elastic waves by rough surfaces". (Click here to download thesis.) EPSRC/DAAD/EU funded.
(Now at Mathematisches Institut II, Universität Karlsruhe, following a year's postdoc at Brunel.)
Dr Mizanur Rahman, PhD awarded November 2000 from Brunel University. "Fast boundary element methods for integral equations on
infinite domains and scattering by unbounded surfaces". (Click here to download thesis.) EPSRC CASE Student
with Radio Communications
Research Unit, Rutherford Appleton Laboratory. (Now
Analyst Programmer (Credit Risk Management Systems), Global Markets, HSBC Bank Plc, email: mizanur.rahman@hsbcgroup.com)
Dr Anja Meier, PhD awarded May 2001 from Brunel University. "Numerical treatment of integral equations on the real line with application to acoustic scattering by unbounded rough surfaces". (Click here to download thesis.) EPSRC CASE Student with
Transport
Research Laboratory. (Now at SAP AG in Walldorf, Germany.)
Dr Claire Lines, PhD awarded July 2003 from Brunel University. "Inverse scattering by unbounded rough surfaces". (Click here to download thesis.) EPSRC CASE Student with Radio Communications
Research Unit, Rutherford Appleton Laboratory.
Previous Post-Doctoral Research Fellows
Professor Bo Zhang, January 1995 to November 1997. EPSRC funded.
Project title "Integral equations on the real line with application
to diffraction grating and related problems".
(Now Professor in Applied Mathematics at the
University of Coventry and Professor in the Chinese Academy of Sciences.)
Dr Tilo Arens. October 2000 to September 2001.
EPSRC Mathematics Postdoctoral Research Fellow. Project title: "Fast numerical methods for integral equations and their application in direct and inverse scattering problems". (Now at Mathematisches Institut II, Universität Karlsruhe.)
Dr Steve Langdon. EPSRC funded Postdoctoral Research Fellow.
Project title "Integral
equation methods for direct and inverse scattering by unbounded surfaces". (Now a Leverhulme Early Career Research Fellow here at the University of Reading.)
Current Research Students and Staff
Current Research Staff
Dr Marko Lindner, EU Marie Curie Research Fellow (from 1st November 2005). Project Title "Wave scattering in unbounded domains: operator algebra and limit operator techniques"
Current Students
Bouazza Birbiad, PhD Student (at Brunel University): Fast integral equation methods for rough surface scattering. Full-time (since 9/2000), EPSRC funded.
Scott La Porte, PhD Student (at Brunel University): Efficient quadrature methods for Green's functions in acoustics. Full-time (since 9/2001), EPSRC funded.
Mark Preston, PhD Student: Boundary integral equation methods for fully nonlinear water waves. Full-time (since 1/2004), EPSRC funded.
Martin Thomas, PhD Student: Variational methods for rough surface scattering. Full-time (since 9/2004), EPSRC funded.
Waves 2003 Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, June 30 - July 4, 2003, University of Jyväskylä, Finland.
Secondary Education at Manchester Grammar School and Colchester Royal
Grammar School.
BSc Maths, Imperial College, London. MSc Engineering Maths, University
of Newcastle-upon-Tyne. PhD on "Ground Effects in Environmental Sound
Propagation"
at University of Bradford.
Lecturer in Mathematics, Coventry Polytechnic, 1987-1989.
Lecturer in Civil Engineering, University of Bradford, 1989-1993.
Lecturer in Mathematics, Brunel University, 1994-96.
Promoted to Senior Lecturer in Mathematics, Brunel University, October
1996.
Awarded 1996 Tyndall Medal of the Institute of Acoustics, November 1997.
Promoted to Reader in Applied Mathematics, Brunel University, October 2000.
Appointed Professor of Applied Mathematics, University of Reading, September 2003.