Investigation of scattering properties of large-scale aperiodic tilings using a combination of the characteristic basis function and adaptive integral methods

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.