Analysis of frequency selective surfaces using two-parameter generalized rational Krylov model-order reduction

Generalized rational Krylov model-order reduction techniques are applied to the spectral Galerkin system describing frequency selective surfaces, resulting in surface reflection coefficient models that depend on both the frequency and the incident angle of the exciting wave. The procedure is composed of three steps: construction of the spectral Galerkin system, linearization of that system, and reduction of the linearized system. The linearization of the spectral Galerkin matrix is carried out using two-dimensional (2-D) polynomial interpolation and the generation of a "two-parameter" companion form of the polynomial system. The subsequent model-order reduction is based on the concept of generalized Krylov subspaces, which are defined in the text. It results in a small system with a frequency and incident angle dependent output that matches the two-parameter polynomial interpolant system transfer function and its derivatives at many points in the frequency/incident angle plane. The technique is applied to the characterization of several frequency selective surfaces, and numerical results that demonstrate the accuracy of the techniques over a broad band of frequencies and range of incident angles are presented.