Browsing by Author "Sewraj, Keshav"

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    Adaptive cross approximation methods for fast analysis of Antenna Arrays
    (Stellenbosch : Stellenbosch University, 2021-03) Sewraj, Keshav; Botha, Matthys M.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
    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.
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    Extensions to the characteristic basis function method, for antenna array analysis
    (Stellenbosch : Stellenbosch University, 2018-03) Sewraj, Keshav; Botha, Matthys M.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
    ENGLISH ABSTRACT: The focus of this work is to solve for the electromagnetic problem of large linear antenna arrays efficiently and accurately within the context of two-dimensional (2D), transverse magnetic (TM) Method of Moments (MoM). Provided that the meshing size is small enough, the MoM can provide accurate results for electromagnetic simulations. However, the memory storage and computational time scale as O(N2) and O(N3) respectively, where N is the number of basis functions. The electrical size solvable with given computational resources is therefore limited. To analyze large antenna arrays, the Characteristic Basis Function Method (CBFM) is employed. This technique decomposes the entire geometry into subdomains, over which, physics-based macro basis functions called CBFs are defined. By using macro basis functions, the aim is to define the same electromagnetic problem using fewer degrees of freedom as compared to the standard MoM. Firstly, a CBFM code where a subdomain is defined to be an antenna element is implemented. The results of CBFM using up to quaternary CBFs (higher-order CBFs) are compared to that of the MoM. Secondly, CBFM with larger overlapping subdomains which span multiple antenna elements in an array is defined, so as the mutual coupling in dense antenna arrays is better represented. To generate higher-order CBFs, the distance-based criterion is proposed which is found to be a more efficient procedure than the conventional tree-based approach, for larger subdomain CBFM. The results for larger subdomain CBFM including the distancebased criterion are compared to the conventional single antenna subdomain CBFM over a range of frequencies.