An effective method for solving the hyper‐singular integral equations in 3‐D acoustics

The application of the boundary integral methods to the problem of acoustics, exterior to a three‐dimensional surface, suffers, in general, from the nonexistence of nonuniqueness of its solutions at frequencies that are characteristic of the associated interior problem. The formulation that is most suitable for numerical implementation still appears to be that proposed by Burton and Miller [Proc. R. Soc. London Ser. A 323, 201–210 (1971)]. However, the hypersingular kernels present in such a formulation render it computationally unattractive. Previous attempts to regularize such hypersingular kernels involved the use of double surface integrals, or implicit use of tangential operators, or closed‐form evaluations of hypersingular integrals. The method of double surface integrals is computationally highly inefficient, even though it allows higher‐order interpolation schemes on the surface. The other two approaches are more conducive to the assumption of a constant value for each of the variables (pressure a...