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

Research output: Contribution to journalArticle

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 integral equation formulation and proving uniqueness of solution for the boundary value problem.

Details

Authors
External organisations
  • University of Reading
  • KTH Royal Institute of Technology
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Fluid Mechanics and Acoustics

Keywords

  • Boundary integral equations, Half-plane, Helmholtz equation, Uniqueness
Original languageEnglish
Pages (from-to)79-88
Number of pages10
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume85
Issue number2
Publication statusPublished - 2005 Feb
Publication categoryResearch
Peer-reviewedYes
Externally publishedYes