Improving the Accuracy of the Boundary Integral Method Based on the Helmholtz Integral

Several recent papers in the literature have been based on various forms of the Helmholtz integral to compute the radiation fields of vibrating bodies. The surface integral form is given. The symbols of P,R micron, rho,G,R,V, and S micron are acoustic pressure, source coordinate, angular frequency, fluid density, Green function, field coordinate, surface velocity and body surface respectively. A discretized form of the surface integral is also given. Solutions to the surface integral are complicated with the singularity of the Green function at R=R micron and with the uniqueness problem at interior eigen frequencies of the enclosed space. The use of the interior integral circumvents the singularity problem since the field points are chosen in the interior space of the vibrating body where a zero pressure condition exists. The interior integral form is given. The method to improve the accuracy is detailed. Examples of the method is presented for a variety of radiators.