A study on avoiding hyper-singular integrals in exterior acoustic radiation analysis

Burton and Millerʹs formulation (BMF) is well known for solving non-uniqueness problems in an exterior acoustic problem. In this paper, an IBMF (improved BMF) is presented by directly taking into account of the normal derivatives of solid angles on the surface. The introduction of the normal derivative of solid angles in building the Burton and Millerʹs formulation will cause the elimination of hyper-singular terms. Here lies the advantage of improved formulation. Then, reproduction of diagonal terms (RDT) is applied to further improve singular integral in IBMF. Three cases are compared for closed axi-symmetric surfaces, including SHF (conventional surface Helmholtz formulation), IBMF and IBMF–RDT. Numerical results show that the combined scheme of IBMF–RDT is valid at all wave numbers, and gives satisfied calculating accuracy, which is about 10 times higher than that of SHF.