Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-30T20:39:38.931Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of the PML equations in general convex geometry

Published online by Cambridge University Press:  12 July 2007

Matti Lassas  and
Erkki Somersalo
Matti Lassas
Affiliation:
Rolf Nevanlinna Institute, University of Helsinki, Helsinki, PO Box 4, FIN-00014, Finland
Erkki Somersalo
Affiliation:
Department of Mathematics, Helsinki University of Technology, Helsinki, PO Box 1100, FIN-02015, Finland
Get access Rights & Permissions [Opens in a new window]

Abstract

In this work, we study a mesh termination scheme in acoustic scattering, known as the perfectly matched layer (PML) method. The main result of the paper is the following. Assume that the scatterer is contained in a bounded and strictly convex artificial domain. We surround this domain by a PML of constant thickness. On the peripheral boundary of this layer, a homogenous Dirichlet condition is imposed. We show in this paper that the resulting boundary-value problem for the scattered field is uniquely solvable for all wavenumbers and the solution within the artificial domain converges exponentially fast toward the full-space scattering solution when the layer thickness is increased. The proof is based on the idea of interpreting the PML medium as a complex stretching of the coordinates in Rn and on the use of complexified layer potential techniques.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 5 , October 2001 , pp. 1183 - 1207
Copyright
Copyright © Royal Society of Edinburgh 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)