Galerkin Boundary Integral Analysis for the 3D Helmholtz Equation

A linear element Galerkin boundary integral analysis for the three-dimensional Helmholtz equation is presented. The emphasis is on solving acoustic scattering by an open (crack) surface, and to this end both a dual equation formulation and a symmetric hypersingular formulation have been developed. A...

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Bibliographic Details
Published inComputer methods in applied mechanics and engineering Vol. 58; no. 3
Main Authors Swager, Melissa, Gray, Leonard J, Nintcheu Fata, Sylvain
Format Journal Article
LanguageEnglish
Published United States 01.01.2010
Subjects
ACOUSTICS
ALGORITHMS
ELEMENTS
EQUATIONS
EVALUATION
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
INTEGRALS
SCATTERING
SERIES EXPANSION
SOLUTIONS
SURFACES
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Summary:A linear element Galerkin boundary integral analysis for the three-dimensional Helmholtz equation is presented. The emphasis is on solving acoustic scattering by an open (crack) surface, and to this end both a dual equation formulation and a symmetric hypersingular formulation have been developed. All singular integrals are defined and evaluated via a boundary limit process, facilitating the evaluation of the (finite) hypersingular Galerkin integral. This limit process is also the basis for the algorithm for post-processing of the surface gradient. The analytic integrations required by the limit process are carried out by employing a Taylor series expansion for the exponential factor in the Helmholtz fundamental solutions. For the open surface, the implementations are validated by comparing the numerical results obtained by using the two different methods.
Bibliography:DE-AC05-00OR22725
USDOE Office of Science (SC)
ISSN:0045-7825
1879-2138