Multiple scattering and modified Green’s functions

Exterior boundary-value problems for the Helmholtz equation can be reduced to boundary integral equations. It is known that the simplest of these fail to be uniquely solvable at certain ‘irregular frequencies.’ For a single smooth scatterer, it is also known that irregular frequencies can be eliminated by using a modified fundamental solution, one that has additional singularities inside the scatterer. This approach is extended to treat the three-dimensional exterior Neumann problem for any finite number of disjoint smooth scatterers, using a fundamental solution that has additional singularities inside every scatterer.  2002 Elsevier Science (USA). All rights reserved.