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The Transmission Problem for the Helmholtz Equation in R³

Andreas Kleefeld

Abstract

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.

Received: 2011-10-5
Revised: 2012-02-10
Accepted: 2012-03-11
Published Online: 2012
Published in Print: 2012

© Institute of Mathematics, NAS of Belarus