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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 12, Issue 3


The Transmission Problem for the Helmholtz Equation in R³

Andreas Kleefeld


The problem under consideration is the three-dimensional transmission problem for time harmonic acoustic waves for two homogeneous media. A simply-connected and bounded region with sufficiently smooth boundary is immersed in an infinite {medium. Each medium is c haracterized by the space independent wave number κ and the density μ.} The system of boundary integral equations is reviewed as well as an existence and uniqueness result. The system is approximated by the boundary element collocation method and consistency, stability, and convergence is proved. In addition, superconvergence is proved and numerical results illustrate the agreement with these theoretical results. No numerical results seem to be reported for this method yet.

Keywords: Helmholtz's equation; integral equation; transmission problem; boundary element method; superconvergence

About the article

Received: 2011-10-05

Revised: 2012-02-10

Accepted: 2012-03-11

Published in Print:

Citation Information: Computational Methods in Applied Mathematics Comput. Methods Appl. Math., Volume 12, Issue 3, Pages 330–350, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.2478/cmam-2012-0008.

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