a Three-Dimensional Hybrid Finite Element/boundary Element Method for the Unified Radiation and Scattering Analysis of Arbitrary Infinite Periodic Arrays.

In this thesis, we present a rigorous frequency domain electromagnetic variational formulation for the non-self-adjoint infinite array problem. The approach presented herein is unified in the sense that it simultaneously addresses both the radiation as well as the scattering analysis of arbitrary infinite periodic array structures. Due to the assumption of infinite periodicity, the analysis focuses on a single unit periodic volume cell which may be arbitrarily filled with 3D perfect and/or lossy electric and magnetic conductors and media (possibly anisotropic), and electromagnetic sources. The array may also be excited from within or without by a incident modal electromagnetic wave. The variational formulation extends the 'variational electromagnetics' (VEM) methodologies of Jeng and the partial variational principle (PVP) concept of Chung in the context of the 3D vector periodic array problem. As such, the tangential field continuity and boundary conditions are explicitly included in the stationary E-field functional. In addition, the generalized periodic boundary conditions are also included in a natural way. A vector Floquet boundary element harmonic expansion has been formulated to represent the radiating free-space trial fields. This permits a proper truncation of the periodic computational domain which strongly enforces the exact radiation boundary condition while simultaneously maintaining the variational nature of the formulation. A tangential vector finite element discretization has been used for the expansion of the periodic volume interior region trial fields. This hybrid combination results in a very general technique for modeling both the 3D geometric complexity as well as the complex electromagnetic physical phenomena associated with general periodic array structures such as frequency selective surfaces (fss), periodic absorbers and phased array antennas. The FEM/BEM discretization process produces a large, semi-space system matrix which is in general complex, nonsymmetric and non -Hermitian. An efficient SSOR-QMR algorithm has been implemented to iteratively solve this complex system. The formulation and numerical implementation has been validated by comparing our computed results with numerous published data both from measurement as well as alternate numerical formulations. In all cases good agreement has been observed.