Skip to main content
Article thumbnail
Location of Repository

The PML for rough surface scattering

By Simon Neil Chandler-Wilde and Peter Monk


In this paper we investigate the use of the perfectly matched layer (PML) to truncate a time harmonic rough\ud surface scattering problem in the direction away from the scatterer. We prove existence and uniqueness of the solution of the truncated problem as well as an error estimate depending on the thickness and composition of the layer. This global error estimate predicts a linear rate of convergence (under some conditions on the relative size of the real and imaginary parts of the PML function) rather than the usual exponential rate. We then consider scattering by a half-space and show that the solution\ud of the PML truncated problem converges globally at most quadratically (up to logarithmic factors), providing support for our general theory. However we also prove exponential convergence on compact subsets. We continue by proposing an iterative correction method for the PML truncated problem and, using our estimate for the PML approximation, prove convergence of this method. Finally we provide some numerical results in 2D.(C) 2008 IMACS. Published by Elsevier B.V. All rights reserved

Topics: 518
Publisher: Elsevier
Year: 2009
OAI identifier:

Suggested articles


  1. (1994). A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,
  2. (2002). 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,
  3. (2001). A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems, doi
  4. (2006). A time domain analysis of PML models in acoustics,
  5. (1978). A variational formulation for exterior problems in linear hydrodynamics, doi
  6. (2003). An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures,
  7. (2006). Analysis of rough surface scattering problems,
  8. (2001). Analysis of the PML equations in general convex geometry, doi
  9. (1998). Diffraction in periodic structures and optimal design of binary gratings I: Direct problems and gradient formulas, doi
  10. (2005). Existence, uniqueness and variational methods for scattering by unbounded rough surfaces,
  11. (1999). Linear Integral Equations, doi
  12. (1995). Mathematical studies in rigorous grating theory,
  13. (2001). Numerical simulation methods for rough surface scattering, doi
  14. (2005). On radiation conditions for rough surface scattering problems,
  15. (1998). On the existence and convergence of the solution of pml equations, doi
  16. (2001). Rigorous solutions for electromagnetic scattering from rough surfaces, doi
  17. (2002). Scattering by rough surfaces,
  18. (1998). The Green’s function for the two-dimensional Helmholtz equation in periodic domains,
  19. (2007). The mathematics of scattering by unbounded, rough, inhomogeneous layers,
  20. (1998). The perfectly matched layer in curvilinear coordinates,
  21. (1991). Theory of Wave Scattering from Random Rough Surfaces, Adam Hilger, doi
  22. (1998). Wave Scattering from Rough Surfaces, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.