IJPAM: Volume 72, No. 3 (2011)
BOUNDARY INTEGRAL EQUATION METHODS
FOR ACOUSTIC SCATTERING
Department of Mathematics and Statistics
Sultan Qaboos University
P.O. Box 36, Post Code 123, Muscat, OMAN
Abstract. A review of integral equation formulation of the exterior acoustic problem with the hard boundary condition is presented. For comparison, three particular methods for the numerical determination of boundary values are considered, viz. Burton and Miller method [#!1!#], Schenck method [#!8!#] and the Modified Layer Formulation Method [#!5!#] (MLF). The Burton and Miller basically incorporates the results of Terai [#!9!#] and combines the surface Helmholtz equation with its normal derivative form. Both Burton and Miller, and Schenck fail for structure surfaces that are plate-like, nevertheless, the Burton and Miller approach is suitable for thinner plates. Schenck approach faces problems with the selection of interior collocation points at higher frequencies, however, Burton and Miller faces no such problems provided the surface mesh is sufficiently fine. Unlike the other two, the MLF method utilizes layer potentials. This method circumvents the hyper-singularity problem and the non-uniqueness problem at a much reduced cost.
Received: March 12, 2011
AMS Subject Classification: 35J05, 45B05
Key Words and Phrases: Helmholtz equation, collocation method, boundary integral equation
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395