3D acoustic wave simulation using BEM formulations: Closed form integration of singular and hypersingular integrals

Among the obstacles to applying boundary element techniques to three-dimensional wave propagation problems is the difficulty of accurately representing the singular and hypersingular terms at the points of application of the virtual loads. This paper presents the analytical evaluation of the singular and hypersingular integrals for constant boundary elements. First, the singular integral results are compared with those evaluated by means of a Gaussian quadrature scheme, which uses an enormous amount of sampling points. In the case of hypersingular integrals the comparison makes use of the results provided by the method presented by Terai [T. Terai, On calculation of sound fields around three dimensional objects by integral equation methods, J Sound Vib 69 (1980) 71–100.]. An additional verification is performed by comparing the boundary element method (BEM) results with known analytical solutions for cylindrical inclusions.