Research on Direct and Inverse Scattering by Rough Surfaces at the University of Reading (and formerly at Brunel University)

An incident TE polarised time harmonic electromagnetic plane wave (left) hitting a periodic perfectly conducting surface, and the scattered wave that is produced (right).

These calculations were carried out by Tilo Arens and Anja Meier using a new integral equation formulation and super-algebraically convergent discretisation scheme described in "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 Applications 12, 281-321.

Copy of a recent talk (May 2005) at the University of Goettingen on "The Mathematics of Scattering by Unbounded Rough Surfaces".

Current group members:

• Professor Simon Chandler-Wilde
• Professor Dr Roland Potthast, to join us from 1st April 2006.
• Dr Stephen Langdon, Leverhulme Early Career Research Fellow
• Dr Marko Lindner, EU Marie Curie Research Fellow, working on "Wave scattering in unbounded domains: operator algebra and limit operator techniques".
• Bouazza Birbiad, EPSRC PhD Student
• Scott La Porte, EPSRC PhD Student
• Martin Thomas, EPSRC PhD Student

• Professor Peter Monk, Department of Mathematical Sciences, University of Delaware, July-August 2005.

• Dr Tilo Arens, EPSRC Maths Poctdoctoral Fellow, Sept 2000-Sept 2001.
• Professor Dr Roland Potthast, EPSRC-funded Postdoctoral Fellow, April 2000-April 2001.
• Professor John DeSanto, School of Mathematical and Computer Sciences, Colorado School of Mines, February-April 2001.
• Professor David Natroshvili, Department of Mathematics, Georgian Technical University, Tbilisi. September 2000-January 2001.

• Dr Kai Haseloh, Institut für Angewandte Mathematik, Universität Hannover
• Professor Kirill Horoshenkov & Professor David Hothersall, School of Engineering, Design, and Technology, University of Bradford. (Funded by EPSRC.)
• Prof Dr Andreas Kirsch, Mathematisches Institut II, Universität Karlsruhe. (Funded by British Council/DAAD.)
• Dr Andrew Peplow, Applied Analysis and Computation Group, Imperial College London.
• Professor Bo Zhang, School of Mathematical and Information Sciences, University of Coventry, and Chinese Academy of Sciences. (Funded by EPSRC.)
• Professor Greg Watts, Transport Research Laboratory, Crowthorne, Berks. (Funded by EPSRC.)

• Development of rigorous mathematical formulations for problems of time harmonic scattering by unbounded rough surfaces, including formulation of radiation conditions, existence and uniqueness results, and stability bounds.
• Proposal and analysis of novel boundary integral equation formulations, including proofs of equivalence with the boundary value problems, existence, uniqueness, and stability questions.
• Arising out of the above, studies of integral operators and integral equations on unbounded domains.
• Development of fast numerical schemes based on integral equation formulations, with attention to: novel discretisation schemes and their analysis; understanding stability. and convergence of truncation of the boundary (the finite section method); iterative solvers; matrix compression issues; analysis of dependence on the wavenumber, k.
• Inverse scattering by rough surfaces and by obstacles buried below such surfaces, whether by iterative, Newton-type methods or by direct, sampling-type methods.
• Weak formulations and combined finite element/boundary element schemes, including study of domain decomposition methods, use of PML.
• Methods for acoustic, electromagnetic, and elastic wave problems.
• Applications to outdoor noise control problems and the modelling of ground penetrating radar.

• Chris Ross, PhD awarded July 1997. "Direct and inverse problems in rough surface scattering". EPSRC funded.
• Philip Morgan, PhD awarded November 1999. "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.
• Tilo Arens, PhD awarded June 2000. "Scattering of elastic waves by rough surfaces". (Click here to download thesis.) EPSRC/DAAD/EU funded.
• Mizanur Rahman, PhD awarded November 2000. "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.
• Anja Meier, PhD awarded May 2001. "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.
• Sumlearng Chunrungsikul, PhD awarded December 2001. "Numerical quadrature methods for singular and nearly singular integrals". (Click here to download thesis.)
• Claire Lines, PhD awarded July 2003. "Inverse scattering by unbounded rough surfaces". (Click here to download thesis.) EPSRC CASE Student with Radio Communications Research Unit, Rutherford Appleton Laboratory.

• The mathematics of scattering by unbounded, rough, inhomogeneous layers.
  S N Chandler-Wilde, P Monk & M Thomas 2005 To appear in Journal of Computational and Applied Mathematics
• A well-posed integral equation formulation for 3D rough surface scattering.
  S N Chandler-Wilde, E Heinemeyer & R Potthast 2006 Published online in Proceedings of the Royal Society of London, Series A DOI: 10.1098/rspa.2006.1752
• On integral equation and least squares methods for scattering by diffraction gratings.
  T Arens, S N Chandler-Wilde & J A DeSanto 2006 Communications in Computational Physics 1, 1010-1042.
• A wavenumber independent boundary element method for an acoustic scattering problem.
  S Langdon & S N Chandler-Wilde 2006 SIAM Journal on Numerical Analysis 43, 2450-2477.
• Acoustic scattering by mildly rough unbounded surfaces in three dimensions.
  S N Chandler-Wilde, E Heinemeyer & R Potthast 2006 SIAM Journal on Applied Mathematics 66, 1002-1026.
• A Brakhage-Werner-type integral equation formulation of a rough surface scattering problem.
  S N Chandler-Wilde, E Heinemeyer & R Potthast 2005 In Advances in Boundary Integral Methods, K Chen (editor), University of Liverpool, pp. 164-173.
• Existence, uniqueness and variational methods for scattering by unbounded rough surfaces.
  S N Chandler-Wilde & P Monk 2005 SIAM Journal on Mathematical Analysis 37, 598-618.
• A time domain point source method for inverse scattering by rough surfaces.
  C D Lines & S N Chandler-Wilde 2005 Computing 75, 157-180.
• Solvability and Fredholm properties of integral equations on the half-line in weighted spaces.
  S N Chandler-Wilde & K O Haseloh 2005 Integral Equations and Operator Theory 51, 5-34.
• A boundary integral equation formulation for the Helmholtz equation in a locally perturbed half-plane.
  S N Chandler-Wilde & A T Peplow 2005 Zeitschrift für Angewandte Mathematik und Mechanik 85, 79-88.
• 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. Published online January 2004, DOI: 10.1098/rsta.2003.1339
• Solvability and spectral properties of integral equations on the real line: II. L^p spaces and applications.
  T Arens, S N Chandler-Wilde, & K O Haseloh 2003 Journal of Integral Equations and Applications 15, 1-35.
• The Dirichlet metaharmonic Green's function for unbounded regions.
  D Natroshvili & S N Chandler-Wilde 2003 Memoirs on Differential Equations and Mathematical Physics 30, 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 Physics 30, 105-146.
• Integral equation methods for scattering by infinite rough surfaces.
  B Zhang & S N Chandler-Wilde 2003 Mathematical Methods in the Applied Sciences 26, 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 A 458, 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 Applications 272, 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 Mathematik 93, 1-51.

(click here to download this paper in pdf format)
• A BMIA canonical grid method for scattering by rough surfaces.
  S N Chandler-Wilde, B Birbiad, & A Meier 2002 Brunel University, Department of Mathematical Sciences, Technical Report TR/03/02, January 2002.
• Uniqueness for Elastic Wave Scattering by Rough Surfaces
  T Arens 2001 SIAM Journal on Mathematical Analysis 33, 461-476.
  
• Point-sources and Multipoles in Inverse Scattering Theory.
  R Potthast 2001. London: Chapman & Hall.
• On the Convergence of Newton's Method in Inverse Scattering.
  R Potthast 2001 Inverse Problems 17, 1419-1434.
• 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 Applications 12, 281-321.
• 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 Applications 245, 28-51.
• 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.

(click here to download this paper in post-script format)
• 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 Acoustics 58, 351-377.
• Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers.

S N Chandler-Wilde & B Zhang 1999 SIAM Journal on Mathematical Analysis 30, 559-583.
(click here to download this paper in post-script format)
• A uniqueness result for scattering by infinite rough surfaces.

S N Chandler-Wilde & B Zhang 1998 SIAM Journal on Applied Mathematics 58, 1774-1790.
(click here to download this paper in post-script format)
• 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.
(click here to download this paper in post-script format)
• 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.
• 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.
• 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.
• 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.

Last updated 5 December 2005