A contribution towards the solution of scattering problems with the fast multipole method

The hybrid procedure which results when the boundary element method is coupled to the method of finite elements is well-suited for the computation of boundary value problems that involve an open domain, where the characterisation of the scattering properties of a cavity-backed aperture in a ground plane represents a problem of practical interest that is considered within the framework of this investigation. The boundary element method enables the restriction of the domain to be discretized with finite elements, but leads to a densely populated matrix which limits the applicability of the hybrid procedure to the solution of problems with a modest number of degrees of freedom on the aperture. This limitation can be lifted by applying the fast multipole method. The present disquisition describes the realisation of a hybrid procedure for the computation of scattering problems where the size of the aperture surface is significantly larger than the wavelength of an incident plane wave. The fast and efficient computation of the interactions between the degrees of freedom on the aperture with the aid of the fast multipole method forms the focal point of the investigation.