Low frequency acoustic and electromagnetic scattering

This paper deals with two classes of problems arising from acoustics and electromagnetics scattering in the low frequency stations. The first class of problem is solving Helmholtz equation with Dirichlet boundary conditions on an arbitrary two dimensional body while the second one is an interior-exterior interface problem with Helmholtz equation in the exterior. Low frequency analysis show that there are two intermediate problems which solve the above problems accurate to 0(k/2/ log k) where k is the frequency. These solutions greatly differ from the zero frequency approximations. For the Dirichlet problem numerical examples are shown to verify the theoretical estimates.