Toward hp-adaptive solution of 3D electromagnetic scattering from cavities

An effective hp-adaptive finite-element (FE) approach is presented for a reliable and accurate solution of 3D electromagnetic scattering problems. The far field is approximated with the infinite-element method. This allows one to reduce the external domain (discretised with finite elements) to a minimum preserving the possibility of arbitrary reduction of the error as the method does not introduce modelling error. The work is focused on scattering from cavity backed apertures recessed in a ground plane. Near optimal discretisations that can effectively resolve local rapid variations in the scattered field can be obtained adaptively by local mesh refinements (so called h-type refinements) blended with graded polynomial enrichments (p-enrichments). The discretisation error can be controlled by a self-adaptive process, which is driven by a posteriori error estimates in terms of the energy norm or in a quantity of interest. The radar cross section (RCS) is an example of the latter. h- and p-adaptively constructed solutions are compared to pure uniform p approximations. Numerical, highly accurate, and fairly converged solutions for generic cavities are given and compared to previously published results.