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The PML for rough surface scattering

Chandler-Wilde, S. N. and Monk, P. (2009) The PML for rough surface scattering. Applied Numerical Mathematics, 59 (9). pp. 2131-2154. ISSN 0168-9274

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To link to this item DOI: 10.1016/j.apnum.2008.12.007


In this paper we investigate the use of the perfectly matched layer (PML) to truncate a time harmonic rough 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 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.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:1611
Uncontrolled Keywords:Perfectly matched layer; Rough surface; Convergence estimates ELECTROMAGNETIC SCATTERING; FINITE-ELEMENT; EQUATIONS; EXISTENCE; LAYERS
Additional Information:2nd Chilean Workshop on Numerical Analysis of Partial Differential Equations, Univ Concepcion, Concepcion, CHILE, JAN 16-19, 2007


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