We implement the finite element-boundary integral (FE-BI) method for the analysis of infinite antenna arrays. We particularly emphasize the use of a new class of tetrahedral hierarchical mixed-order tangential vector finite elements (TVFEs). Also, the infinite periodic Green's function accelerated by the Ewald transform is used as the kernel of the radiation integral. Periodic boundary conditions (PBCs) for lower (0.5) and higher (1.5) order tetrahedral finite elements are implemented through the element matrix transformation algorithm. It is found that by properly placing higher order elements in regions where high field variations are expected and lower order elements elsewhere, accurate values for the scanning reflection coefficient can be obtained with relatively coarse discretizations. This is particularly true for scanning angles away from blindness. To improve field modeling around scan blindness, higher order elements should be placed throughout the unit cell. This way, power transfer between neighboring cells is more accurately modeled. Due to the hierarchical nature of the employed vector basis functions, the extension of the PBC algorithm from lower to higher order elements is fairly straightforward, requiring reordering of the nodes along the faces on opposite unit cell boundaries so that continuity of the tangential fields is preserved.
