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An efficient methodology is introduced for rapid analysis and design of three-dimensional (3-D) doubly periodic structures over a wide frequency range based on hybrid finite element boundary integral (FEBI) methods. The 3-D doubly periodic structures can be represented as nonorthogonal lattices composed of general inhomogeneous bianisotropic media with arbitrarily-shaped metallic patches. Based on Floquet theory and periodic boundary conditions, the original stated problem that involves infinite periodic structures can be converted into a single unit cell. Using the equivalence principle, the derived BI equation formulation is applied to the top and bottom surfaces of the unit cell, which results in a perfectly reflectionless boundary condition for the FE-based approach. Then, the unit cell was meshed using triangular prismatic volume elements, which provide a great deal of flexibility in modeling complex planar geometries with arbitrary shapes in the transverse direction. The adaptive integral method (AIM) was employed to accelerate the calculation of the matrix-vector product for the BI portion within the iterative solver. Furthermore, a model-based parameter estimation (MBPE) technique was proposed for the wide-band interpolation of the required impedance matrix elements in the BI part for near field components that were used in the AIM procedure. The accuracy and efficiency of the proposed hybrid algorithms are demonstrated by the presented numerical results (e.g., in comparison with analytical solutions). Several simulation results are presented to illustrate the flexibility of the proposed methods for analysis of frequency selective surfaces with arbitrarily-shaped metallic patches, bianisotropic materials, and nonorthogonal lattice configurations. [ABSTRACT FROM PUBLISHER]

This paper presents a hybrid approach for efficient analysis of electromagnetic (EM) scattering from large-scale aperiodic structures (e.g., aperiodic Penrose and Danzer tilings), which integrates the characteristic basis function method (CBFM) and the adaptive integral method (AIM). By performing a domain decomposition, a series of characteristic basis functions (CBFs) that are defined on a macro block and comprised of a relatively large number of sub-domain basis functions facilitate a substantial reduction in the method of moments (MoM) matrix size, enabling the use of a direct solver for large problems. The AIM is applied to accelerate the calculation of CBFM-reduced MoM matrices, significantly decreasing the CPU time and memory required for solving large-scale problems. As the size of one block becomes electrically large, the original CBFM combined with the AIM is employed to generate the initial CBFs by solving a large problem with multiple excitations, which results in efficiently constructing the final CBFs afforded by the singular value decomposition (SVD) procedure. This methodology produces a two-level “CBFM + AIM” hybrid algorithm for efficiently characterizing large-scale objects. The numerical results presented demonstrate the accuracy and efficiency of the proposed hybrid algorithm. Then, the developed solver is applied to investigate EM scattering properties of large-scale aperiodic tilings. The numerical results show that Penrose/Danzer tilings exhibit significantly improved grating lobe suppression as compared to their periodic counterparts. [ABSTRACT FROM PUBLISHER]