The design of microwave absorbers with high order hybrid finite element method

A 3D formulation is presented which is based on the periodic hybrid finite element method (PHFEM). Higher-order vector elements are utilized to improve the accuracy. In this method the finite element mesh is truncated by the periodicity boundary conditions (PBC) at the sidewalls and by periodic radiation boundary conditions (RBC) at the top and bottom boundaries of the unit cell. Once again, this being a 3D FEM formulation allows the handling of discontinuities in-geometry and filling material easily. The major merit of PHFEM is the sparse nature of the resulting system of equations, which saves dramatically on computer memory and CPU time when solving the problem. The RBC enforcement will give rise to two dense matrices, which will typically destroy the sparse character to some degree. However, in the case of the microwave absorber, the unit cell is typically tall and skinny, so that the sparsity of the system matrix is most likely preserved. Although each term in the dense matrix associated with the RBC contains an infinite series of Floquet modes, these spectral series converge rapidly and are easy to compute.