Adaptive cross approximation methods for fast analysis of Antenna Arrays

Sewraj, Keshav (2021-03)

Thesis (PhD)--Stellenbosch University, 2021.

Thesis

ENGLISH ABSTRACT: This work is focused on developing efficient numerical electromagnetic algorithms forthe analysis of large antenna arrays, such as being considered as part of the internationalSquare Kilometre Array (SKA) radio astronomy project currently under development.Numerical electromagnetic simulation is a vital tool to evaluate performance during theantenna design process, and it is common to iterate through thousands of simulationsto fine-tune parameters. However, these simulations are often expensive and can be alimiting factor in the available design choices.The Method of Moments (MoM) is a numerical technique used to solve electromag-netic field problems, and is highly suitable for radiation problems such as the analysisof antenna arrays. However, the memory and runtime requirement of the MoM scale asO(N2)andO(N3), respectively, whereNis the number of Degrees of Freedom. As such,electromagnetic analysis performed by the MoM is limited by the electrical size of theproblem. For larger structures, fast MoM-based techniques tailored to specific problemsneed to be devised.In this work, a variety of techniques based on cross approximation is explored andimplemented, for array analysis. In this context, two Directional Cross Approximation(DCA)-based solvers are devised. The DCA is a nested multilevel algorithm which ef-ficiently compresses MoM sub-blocks due to far interactions as a product of low-rankfactors. During the computation of these factors, the far-field is segmented in angularsectors to ensure the numerical rank is limited irrespective of the cluster size.Firstly, the DCA is combined with the Macro Basis Function (MBF) method. In thistechnique, physics-based MBFs are defined over each antenna element, through linearcombinations of the low-level basis functions defined on that domain, in order to createa reduced matrix system, which can then be solved directly. However, one of the MBFsolvers’ bottlenecks is the high cost associated with the computation of reaction terms during the fill-in of the reduced matrix. As such, the DCA algorithm is used to efficientlyrepresent and compute the reaction terms in MBF solvers. The accuracy of using theMBF-DCA solver is validated, and a favorable memory scaling is obtained.Secondly, the single-level version of the DCA is formulated together with a sparsedirect solver scheme, based on the Inverse Fast Multipole Method (IFMM), to solve for antenna array MoM solution directly. The original IFMM formulation is extended forthe directional case, and a new procedure to eliminate and redirect compressible fill-insduring the Gaussian elimination of the sparse matrix is devised.Lastly, a hybrid single-level compression scheme is devised to accelerate the IterativeRadius-Based Domain Green’s Function Method (IRB-DGFM) solver, for array analysis.The compression algorithm combines the standard Adaptive Cross Approximation (ACA)to compress intermediate interactions, and the single-level Nested Cross Approximation(NCA) to represent far interactions efficiently.

AFRIKAANSE OPSOMMING: Hierdie werk fokus op die ontwikkeling van doeltreffende numeriese elektromagnetikaalgoritmes vir die analise van groot antenna samestellings, soos oorweeg word as deel vandie internasionale “Square Kilometre Array (SKA)” radiosterrekunde projek tans onderontwikkeling. Numeriese elektromagnetika simulasie is ’n onontbeerlike gereedskapstukom antenna werkverrigting gedurende die ontwerpsproses te bepaal, aangesien duisendesimulasies dikwels benodig word tydens veelvuldige ontwerpsiterasies. Sulke simulasies isegter tipies duur en kan ’n beperkende faktor tot ontwerpskeuses wees.Die moment metode (MoM) is ’n numeriese tegniek om elektromagnetiese veldpro-bleme op te los en is hoogs gepas vir stralingsprobleme soos die analise van antennasamestellings. Die geheue en looptyd vereistes van die MoM skaleer egter asO(N2)enO(N3), onderskeidelik, waarNdie aantal vryheidsgrade aandui. In die lig hiervanword elektromagnetiese analise met die MoM beperk deur die elektriese grootte van dieprobleem. Vir groter strukture moet versnelde MoM tegnieke wat pasgemaak is vir diespesifieke probleem, geskep word ’n Verskeidenheid van tegnieke gebaseer op kruis-benadering word in hierdie werk on-dersoek, vir samestellingsanalise. Binne hierdie konteks word twee Rigtingsgewyse Kruis-Benadering (RKB)-gebaseerde oplossers daargestel. Die RKB is ’n geneste multivlakalgoritme wat MoM sub-blokke doeltreffend saampers as produkte van lae-rang faktorevir vêr-interaksies. Tydens die bepaling van hierdie faktore word die vêrveld gesegmen-teer in hoeksgewyse sektore wat verseker dat die numeriese range beperk word, ongeagdie tros-grootte.Eerstens word die RKB gekombineer met die Makro Basis Funksie (MBF) metode.Met hierdie tegniek word fisika-gefundeerde MBFs gedefinieer oor elke antenna element,as linieêre kombinasies van die laevlak basis funksies op elke domein, om sodoende ’ngereduseerde matriks stelsel te skep, wat op direkte wyse opgelos kan word. ’n Bottelnekvan die MBF-oplosser is egter die hoë koste verbonde aan die berekening van reaksie-termemet die vul van die gereduseerde matriks. In hierdie verband word die RKB algoritmegebruik om die MBF reaksie-terme doeltreffend te bereken. Die akkuraatheid van dieMBF-RKB oplosser word nagegaan en gunstige geheue-skalering word gedemonstreer. Tweedens word ’n yl-matriks direkte oplossingskema geformuleer wat geskoei is op dieenkel-vlak weergawe van die RKB, vir direkte oplossing van antenna samestelling MoMmatriksvergelykings. Dit is ’n aangepaste weergawe van die Inverse Vinnige MultipoolMetode (IVMM). Die oorspronklike IVMM formulering word uitgebrei na die rigtingsge-wyse geval, en nuwe prosedures vir die eliminasie en herkanalisering van saampersbareinvullings gedurende die Gaussiese eliminasie proses, word daargestel.Laastens word ’n hibriede enkel-vlak saampersingskema daargestel om die IteratieweRadius-Gebaseerde Domein Green Funksie Metode (IRG-DGFM) oplosser te vernel, virsamestellingsanalise. Die saampersingskema kombineer die standaard Aanpassingsvaar-dige Kruis-Benadering (AKB) vir saampersing van intermediêre interaksies, met die enkel-vlak Geneste Kruis-Benadering (GKB) vir doeltreffende saampersing van vêr-interaksies.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/109959
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