A novel finite element-boundary integral (FE-BI) domain decomposition method is applied to the hybrid analysis of large antennas and periodic arrays which may be in the presence of a larger platform, such as an airplane or ship. The FEM is used to model the antenna or array region, and the iterative physical optics (IPO) and the asymptotic phasefront extraction (APEx) methods are used for the larger platform region. The two solutions are coupled via a boundary integral over a surface which separates the two domains. A unique aspect of the formulation is that it allows the FEM and IPO computational meshes to be non-conforming.