Dr Stephen Langdon

Email address: s.langdon@reading.ac.uk

Telephone: +44 (0)118 378 5021

Fax: +44 (0)118 931 3423

UKIE SIAM

Waves 2007, July 23rd-27th 2007

Informal numerical analysis lunchtime seminars

Waves winter workshop, 10th-11th Jan 2007

Numerical Analysis Postgraduate Seminar Day, Friday March 24th 2006, University of Reading

Wave phenomena research at Reading

I am a lecturer in the Department of Mathematics at Reading University. From May 2004 to April 2006 I was a Leverhulme Trust Early Career Fellow.

My main area of research is Numerical Solution of High Frequency Scattering Problems.

As an example, consider the problem of acoustic scattering by an unbounded surface, with piecewise constant surface impedance. This problem models, for example, outdoor sound propagation over inhomogeneous flat terrain. Using a novel Galerkin boundary element method approach, using plane wave basis functions supported on a graded mesh, we recently demonstrated via a rigorous stability and convergence analysis a convergence rate and computational cost independent of the frequency of the incident wave.

To see a video showing (for a particular 2D problem) the incident plane wave (top left), the reflected wave (top right), the total acoustic pressure (bottom left) and the total acoustic pressure minus what it would be if the impedance was constant over the entire surface (bottom right - this corresponds to what we actually compute) click on one of the links below:

(video files best viewed with Windows Media Player (Windows) or xanim (Linux, Unix)). For each problem, the scattering surface is the x-axis of each plot. The surface impedance is constant to the left and right of a central region, on this region (of length 10 wavelengths in the first example, length 20 wavelengths in the second) it takes a different constant value. Thus there are two discontinuities in impedance on the surface, leading to diffracted waves at these points. These diffracted waves can be seen in the plots of the reflected wave (top right) and the total wave subtracting off what it would be if the impedance was constant everywhere (bottom right).

From August 2003 to April 2004 I worked with Professor Mahadevan Ganesh and Professor Ian Sloan on the ARC funded project Advanced computational algorithms for three-dimensional systems at the University of New South Wales in Sydney. Prior to that, I was working with Dr Simon Chandler-Wilde at Brunel University on the EPSRC funded project Integral Equation Methods for Direct and Inverse Scattering by Unbounded Surfaces, and before that I did postdocs at Imperial College London and at Durham University.

Some recent presentations

List of Publications

    Recent preprints, submitted for publication

  1. S. Langdon, M. Mokgolele and S. N. Chandler-Wilde. High frequency scattering by convex curvilinear polygons. To appear in Journal of Computational and Applied Mathematics, (2009), doi: 10.1016/j.cam.2009.08.053.

    2. Journal Publications

  2. S. N. Chandler-Wilde, I. G. Graham, S. Langdon and M. Lindner. Condition number estimates for combined potential boundary integral operators in acoustic scattering. Journal of Integral Equations and Applications, 21, 229-279, (2009).
  3. D. J. Needham, S. Langdon, G. S. Busswell and J. P. Gilchrist. The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory. SIAM J. Appl. Math., 69, 1084-1109, (2009).
  4. J. F. Blowey, J. R. King and S. Langdon. Small- and waiting-time behaviour of the thin-film-equation. SIAM J. Appl. Math., 67, 1776-1807, (2007).
  5. S. N. Chandler-Wilde and S. Langdon. A Galerkin boundary element method for high frequency scattering by convex polygons. SIAM J. Numer. Anal., 45, 610-640, (2007).
  6. M. Ganesh, S. Langdon and I. H. Sloan. Efficient evaluation of highly oscillatory acoustic scattering surface integrals. J. Comput. Appl. Math., 204, 363-374, (2007).
  7. S. Arden, S. N. Chandler-Wilde and S. Langdon. A collocation method for high frequency scattering by convex polygons. J. Comput. Appl. Math., 204, 334-343, (2007).
  8. S. Langdon and S. N. Chandler-Wilde. A wavenumber independent boundary element method for an acoustic scattering problem. SIAM J. Numer. Anal., 43, 2450-2477, (2006).
  9. S. N. Chandler-Wilde, S. Langdon and L. Ritter. A high wavenumber boundary element method for an acoustic scattering problem. Phil. Trans. R. Soc. Lond. A., 362, 647-671, (2004).
  10. J. W. Barrett, S. Langdon and R. Nurnberg. Finite element approximation of a sixth order nonlinear degenerate parabolic equation. Numer. Math., 96, 401-434, (2004).
  11. S. Langdon and I. G. Graham. Boundary integral methods for singularly perturbed boundary value problems. IMA J. Numer. Anal. 21, 217-237, (2001)

    12. Refereed Conference Proceedings

  12. S. N. Chandler-Wilde, S. Langdon and A. Twigger. High frequency boundary element methods for scattering by non-convex obstacles: a model problem, pages 86-87, Proceedings of Waves 2009, the 9th International Conference on Mathematical and Numerical Aspects of Wave Propagation, 15-19 June 2009, Pau, France.
  13. M. Mokgolele, S. Langdon and S. N. Chandler-Wilde, High frequency scattering by a convex polygon with impedance boundary condition, pages 280-281, Proceedings of Waves 2009, the 9th International Conference on Mathematical and Numerical Aspects of Wave Propagation, 15-19 June 2009, Pau, France.
  14. S. N. Chandler-Wilde, S. Langdon and M. Mokgolele. Numerical methods for high frequency acoustic scattering problems. Proceedings of the Institute of Acoustics, Vol.30, pt 2, 2008.
  15. M. Mokgolele, S. N. Chandler-Wilde and S. Langdon. A boundary element method for high frequency scattering by convex curvilinear polygons. Proc. 8th Int. Conf. on Mathematical and Numerical Aspects of Wave Propagation, Reading University, pages 96-98, (2007).
  16. J. M. Melenk and S. Langdon. An hp-boundary element method for high frequency scattering by convex polygons. Proc. 8th Int. Conf. on Mathematical and Numerical Aspects of Wave Propagation, Reading University, pages 93-95, (2007).
  17. S. Langdon, D. Huybrechs and S. N. Chandler-Wilde. A fully discrete collocation method for high frequency scattering by convex polygons. Proc. 8th Int. Conf. on Mathematical and Numerical Aspects of Wave Propagation, Reading University, pages 84-86, (2007).
  18. S. N. Chandler-Wilde, I. G. Graham, S. Langdon and M. Lindner. Condition Number Estimates for Combined Potential Integral Operators in Acoustic Scattering. Proc. 8th Int. Conf. on Mathematical and Numerical Aspects of Wave Propagation, Reading University, pages 47-49, (2007).
  19. S. Langdon and S. N. Chandler-Wilde. Implementation of a boundary element method for high frequency scattering by convex polygons. Proc. 5th U.K. Conf. on Boundary Integral Methods, (K. Chen ed.), pages 2-11, (2005).
  20. S. Langdon, M. Ganesh and I. H. Sloan. Approximation of high frequency acoustic wave surface integrals. Proc. 7th Int. Conf. on Mathematical and Numerical Aspects of Wave Propagation, Brown University, Providece, RI, pages 157-159, (2005).
  21. S. N. Chandler-Wilde and S. Langdon. A boundary element method for high frequency scattering by convex polygons. Proc. 7th Int. Conf. on Mathematical and Numerical Aspects of Wave Propagation, Brown University, Providece, RI, pages 151-153, (2005).
  22. S. Langdon and S. N. Chandler-Wilde. A GTD-based boundary element method for a surface scattering problem. Proceedings of the Institute of Acoustics 25(5), pages 224-233, (2003).
  23. S. Langdon and S. N. Chandler-Wilde. A Galerkin boundary element method for an acoustic scattering problem, with convergence rate independent of frequency. Proc. 4th U.K. Conf. on Boundary Integral Methods, (S. Amini ed.), pages 67-76, Salford University Press (2003).
  24. S. N. Chandler-Wilde, S. Langdon and L. Ritter. A Galerkin boundary element method for a high frequency scattering problem. Proc. 6th Int. Conf. on Mathematical and Numerical Aspects of Wave Propagation, University of Jyväskylä, Finland (G. C. Cohen, E. Heikkola, P. Joly and P. Neittaanmäki, eds), pages 257-262, Springer-Verlag, Berlin (2003).
  25. S. Langdon. A boundary integral equation method for the heat equation. Proc. 5th Int. Conf. on Integral Methods in Science and Engineering (IMSE98), Michigan Technological University, (A. Struthers and B. Bertram, editors), pages 211-216.. Boca Raton FL: CRC (2000).

    26. Other publications

  26. Domain Embedding Boundary Integral Equation Methods and Parabolic PDEs, Ph.D. Thesis, University of Bath, 1999.
  27. S. Langdon, N. Biggs, P. Chamberlain and J.-R. Li, Editorial for Waves 2007 conference, Journal of Computational and Applied Mathematics, (2009), doi: 10.1016/j.cam.2009.08.006.

Last modified 1/12/2009