Exterior acoustic scattering/radiation without interior eigenvalue problems

Abstract

The use of integral equation formulations, such as boundary‐element methods or T‐matrix methods, for the solution of time harmonic exterior acoustic radiation or scattering is hindered by the presence of the “fictitious interior eigenvalue” difficulty that causes the basic integral equation formulation, and thus any numerical scheme based on such a formulation, to fail at certain frequencies related to the interior acoustic problem. A number of techniques have been developed in the last 20 years to circumvent this difficulty; these involve additional computational effort. A method is presented here that eliminates this difficulty analytically by embedding the original obstacle in an infinite acoustic fluid bounded by a simple surface of sources and/or doublets. Such an approach moves the eigenvalue failures from those for the original shape, which are in general unknown, to those for a simple shape which are known. These eigenvalues can be carried through the formulation analytically and canceled exactly, thereby eliminating any subsequent numerical failures.