  A fast full-wave simulation technique is presented for the analysis of large
irregular planar arrays of identical 3-D metallic antennas. The solution method
relies on the Macro Basis Functions (MBF) approach and an interpolatory
technique to compute the interactions between MBFs. The Harmonic-polynomial
(HARP) model is established for the near-field interactions in a modified
system of coordinates. For extremely large arrays made of complex antennas, two
approaches assuming a limited radius of influence for mutual coupling are
considered: one is based on a sparse-matrix LU decomposition and the other one
on a tessellation of the array in the form of overlapping sub-arrays. The
computation of all embedded element patterns is sped up with the help of the
non-uniform FFT algorithm. Extensive validations are shown for arrays of
log-periodic antennas envisaged for the low-frequency SKA (Square Kilometer
Array) radio-telescope. The analysis of SKA stations with such a large number
of elements has not been treated yet in the literature. Validations include
comparison with results obtained with commercial software and with experiments.
The proposed method is particularly well suited to array synthesis, in which
several orders of magnitude can be saved in terms of computation time.
