A boundary integral equation formulation for the Helmholtz equation in a locally perturbed halfplane
(2005) In ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik 85(2). p.7988 Abstract
In this paper we study the application of boundary integral equation methods to the solution of the Helmholtz equation in a locally perturbed halfplane 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 halfspace. 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 halfplane 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 halfspace. 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
 ChandlerWilde, Simon N. and Peplow, Andrew T. ^{LU}
 publishing date
 200502
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Boundary integral equations, Halfplane, 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
 00442267
 DOI
 10.1002/zamm.200410157
 language
 English
 LU publication?
 no
 id
 1dabad8f699b47a99ff4fa6d8339eeb5
 date added to LUP
 20210215 19:57:34
 date last changed
 20210331 11:23:13
@article{1dabad8f699b47a99ff4fa6d8339eeb5, 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 halfplane 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 halfspace. 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 = {ChandlerWilde, Simon N. and Peplow, Andrew T.}, issn = {00442267}, language = {eng}, number = {2}, pages = {7988}, 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 halfplane}, url = {http://dx.doi.org/10.1002/zamm.200410157}, doi = {10.1002/zamm.200410157}, volume = {85}, year = {2005}, }