INTEGRAL-EQUATION METHODS FOR MULTIPLE-SCATTERING PROBLEMS I. ACOUSTICS

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Abstract
Integral-equation methods are often used to treat the exterior problems of acoustics. It is known that the simplest equations fail to be uniquely solvable at certain frequencies (the irregular frequencies). For a single smooth scatterer, D. S. Jones has shown how any given irregular frequency can be removed by using a foundamental solution which has a finite number of additional singularities inside the scatterer. This approach is extended here to treat the two-diamensional exterior Neumann problem for a pair of scatterers, using a fundamental solution which has additional singularities inside each of them.A partial generalization of Jones's result is obtained, involving fundamental solutions with an infinite number of singularities inside one scatterer and a finite number inside the other. Similar results can be obtained for the Dirichlet problem, and in three dimensions.

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