Solving the Dirichlet acoustic scattering problem for a surface with added bumps using the Green's function for the original surface

We solve the Dirichlet problem for acoustic scattering from a surface which has been perturbed by the addition of one or more bumps. We build the solution for the bumpy case using the Green's function for the unperturbed surface, and the solution of a local integral equation in which the integration is carried out only over the added bumps. We conclude by giving an alternative formulation of our method for the special case of a bump on a plane.