New method for accurately calculating singular integrals in solving helmholtz boundary integral equation

We present a new method that can calculate the singular integrals encountered in the Helmholtz boundary integral equation associated with sound radiation and scattering for arbitrary nonsmooth three-dimensional bodies. A brief introduction to Helmholtz boundary integral equation and accurate calculation of singular integrals are demonstrated. We employ the second-order interpolation functions proposed by Chien et al[5]. It is perhaps worth mentioning that, although our accurate calculation includes the computation of potential kernels, no extra effort is really involved since these kernels are a subset of the kernels found in the acoustic problems. In order to demonstrate the robustness, accuracy and convergence of the proposed method, two numerical examples of sound radiation from a pulsating sphere and a cube are presented respectively. In both cases good agreement is obtained between the proposed method and closed-form solutions.