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A boundary integral equation formulation for the Helmholtz equation in a locally perturbed half-plane

Chandler-Wilde, Simon N. and Peplow, Andrew T. LU (2005) In ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik 85(2). p.79-88
Abstract

In this paper we study the application of boundary integral equation methods to the solution of the Helmholtz equation in a locally perturbed half-plane with Robin or impedance boundary conditions. This problem models outdoor noise propagation from a cutting onto a surrounding flat plane, and also the harbour resonance problem in coastal engineering. We employ Green's theorem to derive a system of three coupled integral equations. The three unknowns are the pressure on the boundary of the disturbance and the pressure and its normal derivative on the interface with the upper half-space. We prove that the integral equation formulation has a unique solution at all wavenumbers by proving equivalence of the boundary value problem and the... (More)

In this paper we study the application of boundary integral equation methods to the solution of the Helmholtz equation in a locally perturbed half-plane with Robin or impedance boundary conditions. This problem models outdoor noise propagation from a cutting onto a surrounding flat plane, and also the harbour resonance problem in coastal engineering. We employ Green's theorem to derive a system of three coupled integral equations. The three unknowns are the pressure on the boundary of the disturbance and the pressure and its normal derivative on the interface with the upper half-space. We prove that the integral equation formulation has a unique solution at all wavenumbers by proving equivalence of the boundary value problem and the integral equation formulation and proving uniqueness of solution for the boundary value problem.

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author
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type
Contribution to journal
publication status
published
subject
keywords
Boundary integral equations, Half-plane, Helmholtz equation, Uniqueness
in
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
volume
85
issue
2
pages
10 pages
publisher
John Wiley and Sons
external identifiers
  • scopus:14844283859
ISSN
0044-2267
DOI
10.1002/zamm.200410157
language
English
LU publication?
no
id
1dabad8f-699b-47a9-9ff4-fa6d8339eeb5
date added to LUP
2021-02-15 19:57:34
date last changed
2021-03-31 11:23:13
@article{1dabad8f-699b-47a9-9ff4-fa6d8339eeb5,
  abstract     = {<p>In this paper we study the application of boundary integral equation methods to the solution of the Helmholtz equation in a locally perturbed half-plane with Robin or impedance boundary conditions. This problem models outdoor noise propagation from a cutting onto a surrounding flat plane, and also the harbour resonance problem in coastal engineering. We employ Green's theorem to derive a system of three coupled integral equations. The three unknowns are the pressure on the boundary of the disturbance and the pressure and its normal derivative on the interface with the upper half-space. We prove that the integral equation formulation has a unique solution at all wavenumbers by proving equivalence of the boundary value problem and the integral equation formulation and proving uniqueness of solution for the boundary value problem.</p>},
  author       = {Chandler-Wilde, Simon N. and Peplow, Andrew T.},
  issn         = {0044-2267},
  language     = {eng},
  number       = {2},
  pages        = {79--88},
  publisher    = {John Wiley and Sons},
  series       = {ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik},
  title        = {A boundary integral equation formulation for the Helmholtz equation in a locally perturbed half-plane},
  url          = {http://dx.doi.org/10.1002/zamm.200410157},
  doi          = {10.1002/zamm.200410157},
  volume       = {85},
  year         = {2005},
}