Periodic structure analysis using a hybrid finite element method

Abstract

A numerical solution for the time harmonic electromagnetic fields in a unit cell of an infinite, planar periodic structure has been developed and validated. It uses a variation of the hybrid finite element method that includes periodic radiation conditions at the exterior surfaces and periodicity conditions at the unit cell walls inside the structure. This technique allows the method to deal with structures that include inhomogeneous dielectrics and conductors with arbitrary shape and orientation. This paper presents the formulation of the finite element problem and shows the results of test cases involving an inductive screen, an artificial dielectric, and a layered‐dielectric bandgap medium. The results show that the new method is accurate and versatile.

Classical and enriched finite element formulations for Bloch‐periodic boundary conditions

“…• φ i and φ To derive the system matrices corresponding to the discretization of the weak formulation (9) in such a Bloch-periodic basis, one could proceed as in Section 3.1 by modifying the connectivity matrices in the assembly process (with application of appropriate phase factors); however, the same matrices can also be obtained via row and column operations on the standard Neumann matrices. This follows directly from the relation of the Neumann and Bloch-periodic bases, as we now show.…”

Hybrid Finite Element Methods for Array and FSS Analysis Using Multiresolution Elements and Fast Integral Techniques

“…Tsay and Pozar (1998) applied a hybrid MoM/Green's function method for printed arrays capable of modeling various volumetric inhomogeneities within the grounded substrate of a unit cell. D' Angelo and Mayergoyz (1996) and McGrath and Pyati (1996) employed the lowest order tetrahedral tangential vector nite elements (TVFEs) for modeling the electric eld within the unit cell and used a Floquet modal expansion to satisfy the radiation boundary conditions. Lucas and Fontana (1995) used a similar approach but applied tetrahedral TVFEs of order 1.5.…”

A new finite element‐FDTD‐boundary integral equation technique with biconjugate gradient solver for modeling electromagnetic problems in the frequency domain

“…On the one hand, the FE-BIE approaches have become mature by now. In electromagnetic (EM) literature, they have proven their usefulness for a wide range of applications [Volakis et al, 1997;Eibert et al, 1999;Gedney et al, 1992;McGrath and Pyati, 1996;Rogier et al, 1996Rogier et al, , 2000a. On the other hand, FDTD-BIE formalisms proved to be more involved.…”