Abstract
This paper shows how the Kelvin transformation (inversion) may be applied to scattering problems of linear acoustics. First, the Kelvin transformation and its application to problems in three-dimensional potential theory is reviewed. Then the application to scattering problems is presented. This involves transforming the exterior problem for the original scatterer into a succession of interior problems for the transformed surface. The complete low-frequency expansions of both near and far fields are presented in terms of the solutions of these related interior potential problems. Results are presented for Dirichlet, Neumann, and Robin boundary conditions as well as for the transmission problem.
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