A boundary spectral method for solving exterior acoustical problems with hypersingular integrals

A boundary spectral method is developed to solve acoustical problems with arbitrary boundary conditions. A formulation, originally derived by Burton and Miller, is used to overcome the non-uniqueness problem in the high wave number range. This formulation is further modiÞed into a globally non-singular form to simplify the procedure of numerical quadrature when spectral methods are applied. In the present approach, generalized Fourier coe¦cients are determined instead of local variables at nodes as in conventional methods. The convergence of solutions is estimated through the decay of magnitude of the generalized Fourier coe¦cients. Several scattering and radiation problems from a sphere are demonstrated with high wave numbers in the present paper. Copyright