The PML for rough surface scattering

Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283 and Monk, P. (2009) The PML for rough surface scattering. Applied Numerical Mathematics, 59 (9). pp. 2131-2154. ISSN 0168-9274 doi: 10.1016/j.apnum.2008.12.007

Abstract/Summary

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.

Additional Information	2nd Chilean Workshop on Numerical Analysis of Partial Differential Equations, Univ Concepcion, Concepcion, CHILE, JAN 16-19, 2007
Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/1611
Identification Number/DOI	10.1016/j.apnum.2008.12.007
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
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
Publisher	Elsevier
Download/View statistics	View download statistics for this item