Thesis (PhD) -- Stellenbosch University, 2014. / ENGLISH ABSTRACT: This work considers the efficient numerical analysis of large, aperiodic finite antenna arrays. A Method of Moments (MoM) based domain decomposition technique called the Domain Green's Function Method (DGFM) is formulated to address a wide range of array problems in a memory and runtime efficient manner. The DGFM is a perturbation approach that builds on work initially conducted by Skrivervik and Mosig for disjoint arrays on multi-layered substrates, a detailed review of which will be provided in this thesis. Novel extensions considered for the DGFM are as follows: a formulation on a higher block matrix factorisation level that allows for the treatment of a wider range of applications, and is essentially independent of the elemental basis functions used for the MoM matrix formulation of the problem. As an example of this, both conventional Rao-Wilton-Glisson elements and also hierarchical higher order basis functions were used to model large array structures. Acceleration techniques have been developed for calculating the impedance matrix for large arrays including one based on using the Adaptive Cross Approximation (ACA) algorithm. Accuracy improvements that extend the initial perturbation assumption on which the method is based have also been formulated. Finally, the DGFM is applied to array geometries in complex environments, such as that in the presence of finite ground planes, by using the Numerical Green's Function (NGF) method in the hybrid NGF-DGFM formulation. In addition to the above, the DGFM is combined with the existing domain decomposition method, viz., the Characteristic Basis Function Method (CBFM), to be used for the analysis of very large arrays consisting of sub-array tiles, such as the Low-Frequency Array (LOFAR) for radio astronomy. Finally, interesting numerical applications for the DGFM are presented, in particular their usefulness for the electromagnetic analysis of large, aperiodic sparse arrays. For this part, the accuracy improvements of the DGFM are used to calculate quantities such as embedded element patterns, which is a major extension from its original formulation. The DGFM has been integrated as part of an efficient array analysis tool in the commercial computational electromagnetics software package, FEKO. / AFRIKAANSE OPSOMMING: In hierdie werkstuk word die doeltre ende analise van eindige, aperiodiese antenna samestellings behandel. Eindige gebied benaderings wat op die Moment Metode (MoM) berus, word as vetrekpunt gebruik. `n Tegniek genaamd die Gebied Green's Funksie Metode (GGFM) word voorgestel en is geskik vir die analise van `n verskeidenheid van ontkoppelde samestellings. Die e ektiewe gebruik van rekenaargeheue en looptyd is onderliggend in die implementasie daarvan. Die GGFM is 'n perturbasie metode wat op die oorspronklike werk van Skrivervik en Mosig berus. Laasgenoemde is hoofsaaklik ontwikkel vir die analise van ontkoppelde antenna samestellings op multilaag di elektrikums. `n Deeglike oorsig van voorafgaande word in die tesis verskaf. In hierdie tesis is die bogenoemde werk op `n unieke wyse uitgebrei: `n ho er blok matriks vlak formulering is ontwikkel wat dit moontlik maak vir die analise van `n verskeidenheid strukture en wat onafhanklik is van die onderliggende basis funksies. Beide lae-vlak Rao-Wilton-Glisson (RWG) basis funksies, asook ho er orde hierargiese basis funksies word gebruik vir die modellering van groot antenna samestellings. Die oorspronklike perturbasie aanname is uitgebrei deur akkuraatheidsverbeteringe vir die tegniek voor te stel. Die Aanpasbare Kruis Benaderings (AKB) tegniek is onder andere gebruik om spoed verbeteringe vir die GGFM te bewerkstellig. Die GGFM is verder uitgebrei vir die analise van antenna samestellings in `n komplekse omgewing, bv. `n antenna samestelling bo `n eindige grondplaat. Die Numeriese Green's Funksie (NGF) metode is hiervoor ingespan en die hibriede NGF-GGFM is ontwikkel. Die GGFM is verder met die Karakteristieke Basis Funksie Metode (KBFM) gekombineer. Die analise van groot skikkings wat bestaan uit sub-skikkings, soos die wat tans by die \Low- Frequency Array (LOFAR) " vir radio astronomie in Nederland gebruik word, kan hiermee gedoen word. In die werkstuk word die GGFM ook toegepas op `n reeks interessante numeriese voorbeelde, veral die toepaslike EM analise van groot aperiodiese samestellings. Die akkuraatheidsverbeteringe vir die GGFM maak die berekening van elementpatrone vir skikkings moontlik. Die GGFM is by the sagteware pakket FEKO geintegreer.