Fast solution of multi-scale antenna problems for the Square Kilometre Array (SKA) radio telescope using the Characteristic Basis Function Method (CBFM)

We present a numerically efficient technique, called the Characteristic Basis Function Method (CBFM), for computing the scan impedances of antenna elements located inside an electrically large subarray, which is surrounded by (many) other actively phase-steered subarrays. We construct a reduced moment matrix for a single subarray, and modify its entries in a manner that accounts for the mutual coupling between the surrounding subarrays. This enables us to circumvent the difficult problem of having to deal with the entire large array geometry in one step and reduces the total solve time significantly. Furthermore, the reduced moment matrix can be constructed in a time-efficient manner by exploiting the translation symmetry between pairs of Characteristic Basis Functions (CBFs). However, since we propose an overlapping domain decomposition technique for arrays of electrically interconnected antenna elements, symmetry can only be exploited if the mesh partitioning facilitates a one-to-one mapping of CBFs. To fully utilize the translation symmetry, a strategy has been developed to mesh the structure and to take advantage of this geometrical property. A numerical example is presented for a large array of subarrays of Tapered Slot Antennas (TSAs). The proposed method has good accuracy, excellent numerical efficiency, and reduced memory storage requirement.