Hybrid Generalized Finite Element-boundary integral method for aperture design

While the generalized finite element method was introduced to recently for vector electromagnetic problems, several accompanying developments are necessary to permit its application to the analysis of practical problems such as aperture design. These are (i) the integration of these methods with boundary integrals to help impose radiation boundary integrals and (ii) the means to permit the analysis of inhomogeneous domains. The former is difficult largely due to the fact that it is impossible to define an auxiliary function space on the boundary of the domain due to restrictions placed by the Babuska-Brezzi condition. The latter is difficult as one needs to satisfy different conditions on different component of the field. This paper will propose solutions to these problems. Results attesting to their efficacy, particularly in light of aperture design, will be presented at the conference.