Hybrid FE/BI Modeling of 3-D Doubly Periodic Structures Utilizing Triangular Prismatic Elements and an MPIE Formulation Accelerated by the Ewald Transformation

In this paper, we present the formulation of a finite-element/boundary-integral method for the analysis of three-dimensional doubly periodic structures based on arbitrary nonorthogonal lattice configurations. The method starts from a functional description of the field problem where only a single unit cell of the array is considered. This unit cell is meshed with triangular prismatic volume elements and the electric field intensity is discretized with edge-based expansion functions. On the sidewalls of the unit cell, phase boundary conditions are employed to relate the fields on opposing walls of the unit cell. On the top and/or bottom unit-cell planar surfaces, the mesh is terminated using a mixed potential integral equation. The required space-domain periodic Green’s function is calculated after applying the Ewald transformation to convert the slowly converging series representation into two rapidly converging series. The method is validated for simple slot and strip frequency-selective surfaces as well as microstrip dipole arrays. More complex geometries investigated are slot-coupled microstrip patches, photonic bandgap materials, and the so-called “artificial puck plate” frequency-selective surface bandpass structure.