ON the scattering bya cavity in an impedance plane in three dimensions: Boundary integral equations and novel green's function

Abstract

The problem of the field scattered by a cavity embedded in an impedance (or Robin) plane is considered for the three-dimensional Helmholtz equation in acoustics. Its resolution is more complex than for a scatterer above the plane, in particular because the Green's function for the unperturbed plane has a singular part unsuitable for applications below the plane. It is why the free space Green's function is commonly used in boundary integral equations for the cavity, and three unknowns are necessary. We propose here to use a novel Green's function below the impedance plane, which has the advantage to reduce the number of unknowns, and to simplify the problem. This specific Green's function derives from our recent study for passive and active unperturbed impedance planes. The uniqueness property is studied in passive case. The application to a small cavity leads us to new analytical results. © The Author, 2013. Published by Oxford University Press.