Periodic boundary conditions for finite element analysis of infinite phased array antennas

The finite element method (FEM) has been used to solve for the active reflection coefficient of planar phased arrays. One of the key features of the solution is a periodic boundary condition applied to the three-dimensional FEM mesh to represent periodicity in two directions (including skewed grids), thereby satisfying the Floquet condition. This paper presents the formalism for the periodicity condition, and shows some example calculations for illustrative purposes.