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.
(Less)
- author
- Chandler-Wilde, Simon N.
and Peplow, Andrew T.
LU
- publishing date
- 2005-02
- 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 & Sons Inc.
- 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
- 2022-04-19 04:45:55
@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}},
keywords = {{Boundary integral equations; Half-plane; Helmholtz equation; Uniqueness}},
language = {{eng}},
number = {{2}},
pages = {{79--88}},
publisher = {{John Wiley & Sons Inc.}},
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}},
}