Galerkin Boundary Integral Analysis for the 3D Helmholtz Equation

Journal Article · Fri Jan 01 04:00:00 EST 2010 · Computer Methods in Applied Mechanics and Engineering

OSTI ID:980713

Swager, Melissa ^[1]; Gray, Leonard J ^[2]; Nintcheu Fata, Sylvain ^[2]

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1. Emporia State University
2. ORNL

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.

• Research Organization: Oak Ridge National Laboratory (ORNL)
• Sponsoring Organization: SC USDOE - Office of Science (SC)
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 980713
• Journal Information: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: 3 Vol. 58; ISSN 0045-7825; ISSN CMMECC
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ACOUSTICS
ALGORITHMS
ELEMENTS
EQUATIONS
EVALUATION
INTEGRALS
SCATTERING
SERIES EXPANSION
SOLUTIONS
SURFACES