Efficient hybrid algorithms for characterizing 3-D doubly periodic structures, finite periodic microstrip patch arrays, and aperiodic tilings

In this chapter, several efficient hybrid algorithms are proposed for fast characterization of periodic structures composed of bianisotropic media, large-scale finite periodic microstrip patch arrays, and aperiodic tiling structures. The first is a hybrid periodic finite-element/boundary-integral (FEBI) method developed for fast modeling of 3-D doubly-periodic structures with non-orthogonal lattices composed of bianisotropic media with arbitrarily-shaped metallic patches. The generalized FEBI formulations are accelerated through use of the adaptive integral method (AIM) and model-based parameter estimation (MBPE) techniques. The second algorithm extends the accurate sub-entire domain (SED) basis function method and is combined with the mixed potential integral equation (MPIE) for efficient analysis of large-scale finite periodic arrays of microstrip patches with non-orthogonal lattices. The third algorithm is the proposed two-level characteristic basis function method (CBFM) combined with the AIM for efficiently modeling electromagnetic (EM) scattering from large-scale aperiodic structures (e.g. aperiodic Penrose and Danzer tilings). The efficiency and accuracy of each of the hybrid methods proposed above is demonstrated by numerical tests that include the EM scattering from periodic or aperiodic structures, where appropriate for each code. The developed two-level “CBFM+AIM” hybrid algorithm is employed to investigate EM scattering properties from large-scale aperiodic tilings. The numerical results show that Penrose/Danzer tilings exhibit significantly improved grating lobe suppression as compared to their periodic counterparts.