Mathematical Problems in Engineering

Mathematical Problems in Engineering / 1999 / Article

Open Access

Volume 5 |Article ID 678364 | https://doi.org/10.1155/S1024123X99001052

P. A. Krutitskii, "Method of interior boundaries in a mixed problem of acoustic scattering", Mathematical Problems in Engineering, vol. 5, Article ID 678364, 20 pages, 1999. https://doi.org/10.1155/S1024123X99001052

Method of interior boundaries in a mixed problem of acoustic scattering

Received29 Jan 1999
Revised05 Apr 1999

Abstract

The mixed problem for the Helmholtz equation in the exterior of several bodies (obstacles) is studied in 2 and 3 dimensions. The Dirichlet boundary condition is given on some obstacles and the impedance boundary condition is specified on the rest. The problem is investigated by a special modification of the boundary integral equation method. This modification can be called ‘Method of interior boundaries’, because additional boundaries are introduced inside scattering bodies, where impedance boundary condition is given. The solution of the problem is obtained in the form of potentials on the whole boundary. The density in the potentials satisfies the uniquely solvable Fredholm equation of the second kind and can be computed by standard codes. In fact our method holds for any positive wave numbers. The Neumann, Dirichlet, impedance problems and mixed Dirichlet–Neumann problem are particular cases of our problem.

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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