Open Access

ARTICLE

Galerkin Boundary Integral Analysis forthe 3D Helmholtz Equation

M. R. Swager¹, L. J. Gray², S. Nintcheu Fata²

1 Department of Mathematics, Emporia State University, Emporia KS 66801.
2 Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN37831 USA.

Computer Modeling in Engineering & Sciences 2010, 58(3), 297-312. https://doi.org/10.3970/cmes.2010.058.297

Abstract

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 methods.

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