A Symmetric Galerkin Formulation of the Boundary Element Method for Acoustic Radiation and Scattering

Abstract

A symmetric Galerkin formulation of the Boundary Element Method for acoustic radiation and scattering is presented. The basic integral equations for radiation and scattering of sound are derived for structures, which may consist of a combination of a three-dimensional closed part and thin-walled parts. For the numerical solution of these integral equations a Galerkin-type numerical solution scheme is proposed. The evaluation of the weakly-singular and the hypersingular integrals, occurring in this formulation, is addressed briefly. An improved CHIEF-method is employed in order to prevent the singularity of the coefficient matrix of the algebraic system of equations at so-called irregular frequencies. Subsequently, an algorithm for the automatic determination of the number of nodal unknowns at intersections of thin-walled parts of a structure, or of thin-walled parts and the three-dimensional closed part of a structure, is described. The numerical study contains comparisons of analytical solutions for simple academic examples with the numerical results. In addition, a comparison of measured and computed results is presented for a structure, consisting of both a three-dimensional closed part and a thin-walled part.