Book excerpt: This report summarizes our research effort on the development of higher-order hybrid finite element techniques that are capable of simulating large array antennas embedded in inhomogeneous media. The effort led to the development of a suite of FEM-based simulation tools to deal with a variety of array antennas, which include (i) infinitely large periodic phased arrays, (ii) array antennas that are finite in one dimension and infinitely periodic in the other dimension, (iii) finite array antennas with arbitrary array elements, and (iv) conformal array antennas mounted on a large complex platform. The simulation techniques have the following important characteristics: (i) higher-order geometrical modeling, (ii) higher-order field discretization, (iii) hybridization with surface integral equations using fast algorithms, (iv) a highly effective preconditioner, and (v) accurate antenna feed modeling.