Doctoral Degrees (Electrical and Electronic Engineering)

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Browsing Doctoral Degrees (Electrical and Electronic Engineering) by browse.metadata.advisor "Botha, Matthys M."

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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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    Fast Mesh-based physical optics for large-scale electromagnetic analysis
    (Stellenbosch : Stellenbosch University, 2016-12) Xiang, Daopu; Botha, Matthys M.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
    ENGLISH ABSTRACT: At sufficiently high frequencies, the electrical size of scattering objects become very large. The electromagnetic field simulation of such objects becomes prohibitively expensive with physically rigorous (full wave) computational electromagnetics methods. In such cases, methods based on asymptotic assumptions can be employed instead, to approximately solve Maxwell’s equations. The physical optics (PO) approximation for a conducting surface, is a well-known asymptotic assumption. The multiple-reflection PO (MRPO) method is obtained by applying the PO approximation recursively, to model multiple reflections occurring internally to an object. The overall research goal of this work is to significantly accelerate the mesh-based MRPO for electromagnetic scattering analysis. A standard representation was chosen for the surface current, namely Rao- Wilton-Glisson (RWG) basis functions on a mesh of triangle elements. Since the MRPO is an extension of the single-reflection PO (SRPO), the main bottleneck in the SRPO, namely incident field shadowing determination, is addressed first. An adaptive, multilevel, buffer-based shadowing determination algorithm is developed which is robustly optimal, yielding O(N) time-scaling results for extreme test cases (N denotes the number of mesh elements). Secondly, the first ever, comprehensively accelerated version of the meshbased MRPO method (which rigorously takes internal shadowing into account), denoted fast MRPO (FMRPO), is developed. The FMRPO uses the multi-level, fast multipole method (MLFMM) to accelerate internal reflected field calculations. The inter-group interaction criterion of the MLFMM is altered to account for shadowing. Inter-group shadowing status flags are efficiently evaluated. The runtime scaling of the conventional MRPO is O(Nˆ2), while the runtime of the FMRPO scales as quasi-O(N log N), depending on the specific geometry. Results are presented for practical geometries with larger electrical sizes than have ever before been considered with the MRPO, but which can now for the first time be solved in realistically fast runtimes. With the FMRPO there is no fundamental limit to the electrical size of the scattering objects that can be solved.