Doctoral Degrees (Electrical and Electronic Engineering)

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A comparative analysis of the performance and deployment overhead of parallelized Finite Difference Time Domain (FDTD) algorithms on a selection of high performance multiprocessor computing systems
(Stellenbosch : Stellenbosch University, 2013-12) Ilgner, Robert Georg; Davidson, D. B.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
ENGLISH ABSTRACT: The parallel FDTD method as used in computational electromagnetics is implemented on a variety of different high performance computing platforms. These parallel FDTD implementations have regularly been compared in terms of performance or purchase cost, but very little systematic consideration has been given to how much effort has been used to create the parallel FDTD for a specific computing architecture. The deployment effort for these platforms has changed dramatically with time, the deployment time span used to create FDTD implementations in 1980 ranging from months, to the contemporary scenario where parallel FDTD methods can be implemented on a supercomputer in a matter of hours. This thesis compares the effort required to deploy the parallel FDTD on selected computing platforms from the constituents that make up the deployment effort, such as coding complexity and time of coding. It uses the deployment and performance of the serial FDTD method on a single personal computer as a benchmark and examines the deployments of the parallel FDTD using different parallelisation techniques. These FDTD deployments are then analysed and compared against one another in order to determine the common characteristics between the FDTD implementations on various computing platforms with differing parallelisation techniques. Although subjective in some instances, these characteristics are quantified and compared in tabular form, by using the research information created by the parallel FDTD implementations. The deployment effort is of interest to scientists and engineers considering the creation or purchase of an FDTD-like solution on a high performance computing platform. Although the FDTD method has been considered to be a brute force approach to solving computational electromagnetic problems in the past, this was very probably a factor of the relatively weak computing platforms which took very long periods to process small model sizes. This thesis will describe the current implementations of the parallel FDTD method, made up of a combination of several techniques. These techniques can be easily deployed in a relatively quick time frame on computing architectures ranging from IBM’s Bluegene/P to the amalgamation of multicore processor and graphics processing unit, known as an accelerated processing unit.
Design of a dual-polarized dense dipole array for SKA mid-frequency aperture array
(Stellenbosch : Stellenbosch University, 2016-03) Gilmore, Jacki; Davidson, D. B.; Stellenbosch University. Faculty of Engineering. dept. of Electrical and Electronic Engineering.
ENGLISH ABSTRACT: This dissertation presents the design of a dual-polarized Dense Dipole Array, or “DDA”, as a candidate element for the SKA Mid-Frequency Aperture Array. The design consists of tightly coupled dipole elements above a ground plane and is fed differentially through a specially designed commonmode suppressing feed. Apart from the DDA, there are currently three design concepts under evaluation for the SKA Mid-Frequency aperture array as part of the SKA Advanced Instrumentation Program. The strength of the DDA is that it is a planar structure consisting only of a ground plane and an array element layer in addition to the feed structure, while the other geometries are either three layer or three dimensional structures, all of which complicates mass production of the array tiles. The design is an implementation of Wheeler’s current sheet array and based on work by Munk, where a combination of the capacitances between the tips of neighbouring elements and the close proximity of the elements to one another are exploited in order to increase the overall bandwidth of the array. In the first part of the dissertation, the design is restricted to the singlepolarized case and an extensive parameter study is done in order to gain a better understanding of the physics involved. The single-polarized design is then optimised using a commercial genetic algorithm optimiser and simulation results are obtained that indicate that a bandwidth of 3.8:1 is achievable with good impedance behaviour with scan angle. A scan loss of < 5 dB across all in-band frequencies was also demonstrated. The second part of the dissertation expands the single-polarized design to a dual-polarized design. Although difficulties were encountered with the optimisation of the dual-polarized design resulting in a perceived performance penalty from that of the single-polarized case, it is anticipated that performance similar to that of the single-polarized case will be achievable should an optimal design be identified. It has, however, been shown that the stability of the impedance with scan angle as well as the scan loss is still comparable to that of other MFAA front-end concepts. The third part of the dissertation presents a design of an antenna feed that suppresses common-mode resonances commonly encountered in connected antenna arrays. The design makes use of symmetrical wideband microstrip-slotline transitions to cancel out common-mode signals, while differential-mode signals will still propagate through. The design is verified using both simulations and measurements of a manufactured prototype. A wide bandwidth and a CMRR > 30 dB is achieved that exceeds the design specifications set out. Lastly, both the single-polarized as well as the dual-polarized designs are verified using manufactured prototypes. A major contribution of this dissertation is the manufacturing of a 1 m2 dual-polarized DDA prototype. The relatively flat embedded element pattern and good cross-polarization characteristics demonstrated with the large prototype is a crucial performance characteristic in in achieving cost-effective digital beam-forming.
Efficient finite element electromagnetic analysis of antennas and microwave devices : the FE-BI-FMM formulation and a posteriori error estimation for p adaptive analysis
(Stellenbosch : Stellenbosch University, 2002-09) Botha, Matthys Michiel; Davidson, D. B.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
ENGLISH ABSTRACT: This document presents a Galerkin FE formulation for the full-wave, frequency domain, electromagnetic analysis of three dimensional structures relevant to microwave engineering, together with the investigation of two techniques to enhance the formulation's computational efficiency. The first technique considered is the fast multi pole method (FMM) and the second technique is adaptive refinement of the discretization, based on a posteriori error estimation. Thus, the motivation for the work presented in this document is to increase the computational efficiency of the FE formulation considered. The FE formulation considered is widely used within the microwave engineering, finite element community. Tetrahedral, rectilinear, curl-conforming, mixed- and full order, hierarchical vector elements are used. The formulation is extended to incorporate a cavity backed aperture employing the appropriate half-space Green function within a BI boundary condition, which represents a specific member of a large class of hybrid FE-BI formulations. The formulation is also extended to model coaxial ports via a Neumann boundary condition, using a priori knowledge of the dominant modal fields. Results are presented in support of the formulation and its extensions, including novel results on the coupling between microstrip patch antennas on a perforated substrate. The FMM is investigated first, with the purpose of optimizing the non-local BI component of the cavity FE-BI formulation, in light of its coupling with the differential equation based, sparse FEM. The FMM results in a partly sparse factorization of the BI contribution to the system matrix. Error control schemes for the FMM are thoroughly reviewed and an additional, novel scheme is empirically devised. The second technique investigated, which is more directly related to the FEM and larger in scope, is the use of a posteriori error estimation, in order to optimize the FE discretization through adaptive refinement. A overview of available a posteriori error estimation techniques in the general FE literature is given as well as a survey of available techniques that are specifically tailored to Maxwell's equations. Two known approaches within the applied mathematics literature are adapted to the FE formulation at hand, resulting in two novel, residual based error estimation procedures for this FE formulation - one explicit in nature and the other implicit. The two error estimators are then used to drive a single p adaptive analysis cycle of the FE formulation, experimentally demonstrating their effectiveness. A quasi-static condition is introduced and successfully used to enhance the adaptive algorithm's effectiveness, independently of the error estimation procedure employed. The novel error estimation schemes and adaptive results represent the main research contributions of this study.
Efficient high-order time domain finite element methods in electromagnetics
(Stellenbosch : University of Stellenbosch, 2009-03) Marais, Neilen; Davidson, D. B.; University of Stellenbosch. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
The Finite Element Method (FEM) as applied to Computational Electromagnetics (CEM), can beused to solve a large class of Electromagnetics problems with high accuracy and good computational efficiency. For solving wide-band problems time domain solutions are often preferred; while time domain FEM methods are feasible, the Finite Difference Time Domain (FDTD) method is more commonly applied. The FDTD is popular both for its efficiency and its simplicity. The efficiency of the FDTD stems from the fact that it is both explicit (i.e. no matrices need to be solved) and second order accurate in both time and space. The FDTD has limitations when dealing with certain geometrical shapes and when electrically large structures are analysed. The former limitation is caused by stair-casing in the geometrical modelling, the latter by accumulated dispersion error throughout the mesh. The FEM can be seen as a general mathematical framework describing families of concrete numerical method implementations; in fact the FDTD can be described as a particular FETD (Finite Element Time Domain) method. To date the most commonly described FETD CEM methods make use of unstructured, conforming meshes and implicit time stepping schemes. Such meshes deal well with complex geometries while implicit time stepping is required for practical numerical stability. Compared to the FDTD, these methods have the advantages of computational efficiency when dealing with complex geometries and the conceptually straight forward extension to higher orders of accuracy. On the downside, they are much more complicated to implement and less computationally efficient when dealing with regular geometries. The FDTD and implicit FETD have been combined in an implicit/explicit hybrid. By using the implicit FETD in regions of complex geometry and the FDTD elsewhere the advantages of both are combined. However, previous work only addressed mixed first order (i.e. second order accurate) methods. For electrically large problems or when very accurate solutions are required, higher order methods are attractive. In this thesis a novel higher order implicit/explicit FETD method of arbitrary order in space is presented. A higher order explicit FETD method is implemented using Gauss-Lobatto lumping on regular Cartesian hexahedra with central differencing in time applied to a coupled Maxwell’s equation FEM formulation. This can be seen as a spatially higher order generalisation of the FDTD. A convolution-free perfectly matched layer (PML) method is adapted from the FDTD literature to provide mesh termination. A curl conforming hybrid mesh allowing the interconnection of arbitrary order tetrahedra and hexahedra without using intermediate pyramidal or prismatic elements is presented. An unconditionally stable implicit FETD method is implemented using Newmark-Beta time integration and the standard curl-curl FEM formulation. The implicit/explicit hybrid is constructed on the hybrid hexahedral/tetrahedral mesh using the equivalence between the coupled Maxwell’s formulation with central differences and the Newmark-Beta method with Beta = 0 and the element-wise implicitness method. The accuracy and efficiency of this hybrid is numerically demonstrated using several test-problems.
Expanding the field of view: station design for the AAMID SKA radio telescope
(Stellenbosch : Stellenbosch University, 2019-12) Bij de Vaate, Jan Geralt; De Villiers, D. I. L.; Davidson, D. B.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
ENGLISH ABSTRACT: The discovery of radio astronomy dates back to 1928, when Karl Jansky made the first detection of cosmic noise static. Radio astronomy is therefore a relatively young science and its development is completely in parallel with the radio technology enhancements, including the modern information technology. Radio astronomy has been often at the forefront; the first adopters of new technologies and capabilities. Very often radio astronomy triggered inventions that have been of direct use for other sciences and society. With the advent of digital signal processing, faster and smaller computers, radio astronomy has progressed at a very high pace. Arrays are being designed and built that contain thousands of individual antennas, connected and processed with digital signal processing, enabling very high performance. The conception of the Square Kilometre Array can be directly linked to the potential of Aperture Arrays (AA). As early as 1994 first sketches of the Square Kilometre Array consisted of flat electronically steerable panels. This AA telescope, briefly called the HI telescope, after the HI resonant line at 1421 MHz, would run from 150 to 1450 MHz. Although AAs are technically feasible, SKA1 will use dishes for the frequencies above 350MHz. This dissertation addresses the requirements, system design and possible implementation of an AA system for the SKA2, the second phase of the square kilometre array project. Aperture Arrays have the potential of instantaneous all-sky observations, creating a very powerful telescope. However, the realization of this telescope is not without challenges in cost, power consumption and operational performance. The research in this dissertation explores the potential of the sparse-regular array concept. Sparse-regular arrays are in use for lower frequency telescopes but implementation of this concept has not been considered for higher frequencies; up to the HI line at 1421 MHz. It will be argued with a new proposed figure of merit, average sensitivity divided by system cost, that a sparse-regular design can be superior to a dense or sparse-random system. This dissertation therefore provides an alternative solution for aperture arrays for the SKA and in particular focusses on a possible realization. A realization which takes signal processing into account that goes a step further than ‘just’ build a telescope that can do the same as dishes, but a bit better. For this it is proposed to use Fast Fourier Transform signal processing, enabled by a regular antenna placement structure. FFT signal processing will reduce the processing load significantly and fully utilizes the potential of AA’s. Therefore, regular arrays, sparse or dense, will be lower in cost and power consumption and superior in performance when compared to random arrays. This dissertation concludes that the sparse-regular concept, although technically feasible, has a number of significant drawbacks and therefore might not be the design of choice for SKA2.
GPU acceleration of matrix-based methods in computational electromagnetics
(Stellenbosch : University of Stellenbosch, 2011-03) Lezar, Evan; Davidson, D. B.; University of Stellenbosch. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
ENGLISH ABSTRACT: This work considers the acceleration of matrix-based computational electromagnetic (CEM) techniques using graphics processing units (GPUs). These massively parallel processors have gained much support since late 2006, with software tools such as CUDA and OpenCL greatly simplifying the process of harnessing the computational power of these devices. As with any advances in computation, the use of these devices enables the modelling of more complex problems, which in turn should give rise to better solutions to a number of global challenges faced at present. For the purpose of this dissertation, CUDA is used in an investigation of the acceleration of two methods in CEM that are used to tackle a variety of problems. The first of these is the Method of Moments (MOM) which is typically used to model radiation and scattering problems, with the latter begin considered here. For the CUDA acceleration of the MOM presented here, the assembly and subsequent solution of the matrix equation associated with the method are considered. This is done for both single and double precision oating point matrices. For the solution of the matrix equation, general dense linear algebra techniques are used, which allow for the use of a vast expanse of existing knowledge on the subject. This also means that implementations developed here along with the results presented are immediately applicable to the same wide array of applications where these methods are employed. Both the assembly and solution of the matrix equation implementations presented result in signi cant speedups over multi-core CPU implementations, with speedups of up to 300x and 10x, respectively, being measured. The implementations presented also overcome one of the major limitations in the use of GPUs as accelerators (that of limited memory capacity) with problems up to 16 times larger than would normally be possible being solved. The second matrix-based technique considered is the Finite Element Method (FEM), which allows for the accurate modelling of complex geometric structures including non-uniform dielectric and magnetic properties of materials, and is particularly well suited to handling bounded structures such as waveguide. In this work the CUDA acceleration of the cutoff and dispersion analysis of three waveguide configurations is presented. The modelling of these problems using an open-source software package, FEniCS, is also discussed. Once again, the problem can be approached from a linear algebra perspective, with the formulation in this case resulting in a generalised eigenvalue (GEV) problem. For the problems considered, a total solution speedup of up to 7x is measured for the solution of the generalised eigenvalue problem, with up to 22x being attained for the solution of the standard eigenvalue problem that forms part of the GEV problem.
Improving the direction-dependent gain calibration of reflector antenna radio telescopes
(Stellenbosch : Stellenbosch University, 2013-12) Young, Andre; Davidson, D. B.; Maaskant, R.; Ivashina, M. V.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
ENGLISH ABSTRACT: Utilising future radio interferometer arrays, such as the Square Kilometre Array (SKA), to their full potential will require calibrating for various direction- dependent effects, including the radiation pattern (or primary beam in the parlance of radio astronomers) of each of the antennas in such an array. This requires an accurate characterisation of the radiation patterns at the time of observation, as changing operating conditions may cause substantial variation in these patterns. Furthermore, fundamental imaging limits, as well as practical time constraints, limit the amount of measurement data that can be used to perform such characterisation. Herein three techniques are presented which aim to address this requirement by providing pattern models that use the least amount of measurement data for an accurate characterisation of the radiation pattern. These methods are demonstrated through application to the MeerKAT Offset Gregorian (OG) dual-reflector antenna. The first technique is based on a novel application of the Jaco bi-Bessel series in which the expansion coefficients are solved directly from the secondary pattern. Improving the efficiency of this model in the desired application leads to the development of a different set of basis functions, as well as two constrained solution approaches which reduce the number of pattern measurements required to yield an accurate and unique solution. The second approach extends the application of the recently proposed Characteristic Basis Function Patterns (CBFPs) to compensate for non-linear pattern variations resulting from mechanical deformations in a reflector antenna system. The superior modelling capabilities of these numerical basis functions, which contain most of the pattern features of the given antenna design in a single term, over that of analytic basis functions are demonstrated. The final method focusses on an antenna employing a Phased Array Feed (PAF) in which multiple beam patterns are created through th e use of a beam-former. Calibration of such systems poses a difficult problem as the radiation pattern shape is susceptible to gain variations. Here we propose a solution which is based on using a Linearly Constrained Minimum Varia nce (LCMV) beamformer to conform the realised beam pattern to a physics-based analytic function. Results show that the LCMV beamformer successful ly produces circularly symmetric beams that are accurately characterised with a single-term analytic function over a wide FoV.
An investigation into the computer-aided modelling of active microstrip patch arrays
(Stellenbosch : Stellenbosch University, 1998) Williams, Kevin; Reader, H. C.; Davidson, D. B.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
ENGLISH ABSTRACT: Due to the complex nonlinear behaviour of active radiating antennas, very few formal design methods or comprehensive modelling procedures for these modules have been published. This thesis investigates the modelling of these structures using a commercial circuit simulation package, HP-EESof Communications Design Suite, in combination with the Finite-Difference Time-Domain (FDTD) method of computational electromagnetics. A five element active microstrip array composed of aperture-coupled patch antennas fed by individual oscillators is considered. The principle of injection-locking to provide phase control of the oscillators is studied. The frequency-domain harmonic-balance simulator, and a time-domain simulator using convolution to handle microstrip elements are used for the design of the oscillators. Techniques used for the simulation of free-running and injection-locked behaviour are reported, where it is shown that the use of conventional circuit simulation techniques is inadequate. The standard implementation of the harmonic-balance method is found to be unable to predict locking behaviour reliably, while the convolution simulator suffered from long-time instability. An approach based on the Van der Pol analysis is used to simplify the model of the oscillators, and allows the prediction of injection-locking behaviour using the circuit simulators, although this is limited in accuracy. This is achieved by splitting the oscillator into a one-port amplifier and a resonator. A function, extracted from loadpulling simulations, is used to characterise the nonlinear input conductance of the amplifier. The FDTD method is used to analyse the aperture coupled microstrip antennas used as radiators on the array, as well as the complete array. Various pertinent issues regarding the use of the FDTD method to model microstrip circuits, and in particular, aperture-coupled patch antennas are addressed. The Berenger Perfectly Matched Layer (PML) is compared to the well known Mur and dispersive boundary conditions. The implications of limiting the discretisation of components making up an aperture-coupled patch antenna on the accuracy of the computed impedance parameters are investigated. Such components include the microstrip transmission line and the slot. Comparisons to measurements show that the model of the complete array is accurate, even with a relatively coarse mesh.
Karoo Array Telescope site shielding : laboratory, computational and multi-copter studies
(Stellenbosch : Stellenbosch University, 2015-12) Pienaar, Hardie; Reader, H. C.; Davidson, D. B.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering
ENGLISH ABSTRACT: The Northern Cape in South Africa has been chosen to host the Square Kilometre Array (SKA) due to the area’s overall radio quietness. As part of the supporting systems for the Karoo Array Telescope (KAT), a processing building has been constructed on the site. With the Karoo Array Processing Building (KAPB) now in place, investigating the radio frequency interference (RFI) of the building has become a high priority. If successful, understanding of RFI propagation on-site will shape policies and contribute to the sustainability of on-site radio quietness. This dissertation focuses on understanding the shielding and propagation characteristics of both the KAPB building, as well as a man-made soil berm. On-site measurements, scale models and computational models will be used to investigate the local electromagnetic environment. Additionally, a Multi-copter vehicle is developed to support on-site measurement campaigns. Using data measured on-site it was possible to develop empirical models for local shielding estimations. It was found that the shielding performance of the berm was primarily affected by diffraction. Also, the developed computational model makes it possible to investigate alternative terrestrial structures. The work done in this dissertation will permit off-site analysis of propagation over terrestrial structures. Moreover, the development of a Multi-copter measurement platform creates more efficient metrology. Finally, empirical models are designed so that shielding budgets can be calculated for noise sources to the nearest receivers.
The method of manufactured solutions for the verification of computational electromagnetic codes
(Stellenbosch : Stellenbosch University, 2013-03) Marchand, Renier Gustav; Davidson, D. B.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
ENGLISH ABSTRACT: In this work the Method of Manufactured Solutions (MMS) is introduced for the code veri cation of full-wave frequency dependent electromagnetic computational software. At rst the method is sketched in the context of the veri cation and validation process and the need for proper code veri cation is highlighted. Subsequently, the MMS is investigated in its natural context: the Finite Element Method, speci cally for the E- eld Vector Wave Equation. The usefulness of the method to detect error in a computational code is demonstrated. The selection of Manufactured Solutions is discussed and it is demonstrated how it can be used to nd the probable cause of bugs. Mutation testing is introduced and used to show the ability to detect errors present in code. The MMS is nally applied in a novel manner to a Method of Moments (MoM) code. The challenges of numerical integration associated with the application of the operator is discussed and correct integration is successfully demonstrated. Subsequently the MMS is demonstrated to be successfully applied to the MoM and mutation testing is used to demonstrate the practical e cacy of the method. The application of the MMS to the MoM is the main contribution of this work.
A moment method solution of electromagnetic radiation from composite bodies of revolution
(Stellenbosch : Stellenbosch University, 1994) Steyn, Pierre; Davidson, D. B.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
ENGLISH ABSTRACT: Many structures in engineering today use composite materials, combining structural strength with light weight. Electromagnetically, the materials vary from dielectrics, penetrable by electromagnetic fields, to highly conductive types. Additionally the materials can be inhomogeneous, i.e. the electrical properties of the material are a function of location. The requirement is foreseen to be able to predict electromagnetic scattering by such structures, as well as radiation from antennas mounted on them. Analytical solutions of such problems are in many cases impossible and they must be modelled numerically. Examples of such problems are medical applications of electromagnetics and antennas mounted on future vehicles. The main contribution of this dissertation is the demonstration of the suitability of a surface integral equation formulation, solved by a moment method solution, in solving problems involving electromagnetic radiation from composite bodies of revolution. A body of revolution is a body having rotational symmetry and a composite body is defined here as one made up of different homogeneous isotropic material regions, penetrable by electromagnetic waves, and perfectly electrically conducting regions surrounded by free space. The material regions can be lossy. The formulation described here has previously been successfully applied to compute scattering from composite bodies of revolution. In this dissertation the formulation is extended to radiation problems involving apertures mounted in conducting surfaces of the body of revolution. A number of problems can be modelled as bodies of revolution including a number of practical antenna problems. The rotational symmetry of these problems is exploited to reduce the computational requirements of a three dimensional problem to that of a number of two dimensional problems. The dissertation begins with a review of literature on the moment method and bodies of revolution which serves to place the work in context. An overview of the mathematical formulation of the problem, which is based on an application of the equivalence principle, is then presented. The formulation leads to a set of surface integral equations having surface currents as the unknowns to be solved for. A number of integral equation sets are possible depending on choices made in the formulation process. These choices are discussed. The particular integral equation formulation applied in this dissertation is cast into a form readily solvable by the moment method. The numerical solution of the integral equations by way of the moment method is derived giving careful attention to formalizing a notation that simplifies the formidable "book-keeping" problems associated with composite bodies of revolution consisting of many regions. Numerical results are presented for a canonical problem which are compared to analytical solutions. A number of practical antenna configurations are successfully analysed using the formulation. Input impedance and far field results, which are compared with measurements, are presented. Part of the formulation, the integral equations for conducting regions, does not guarantee unique solutions at all frequencies. This problem, commonly known in the literature as the "interior resonance" problem, is evident in the computed results and occurs in the vicinity of discrete frequencies associated with the problem's geometry. A method proposed in the literature for avoiding the problem is evaluated. The method involves detecting the problem frequencies and correcting the computed current at these frequencies. The method can be implemented without having to modify the integral formulation.
A superconducting software defined radio frontend with application to the Square Kilometre Array
(Stellenbosch : Stellenbosch University, 2013-12) Volkmann, Mark Hans; Fourie, C. J.; Davidson, D. B.; Perold, W. J.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
ENGLISH ABSTRACT: Superconducting electronics can make the Square Kilometre Array (SKA) a better instrument. The largest radio telescope in the world will consist of several arrays, the largest of which, consisting of more than 3000 dishes, will be situated primarily in South Africa. The ambitions of the SKA are grand and their realisation requires technology that does not exist today. Current plans see signals in the band of interest ampli ed, channelised, mixed down and then digitised. An all-digital frontend could simplify receiver structure and improve its performance. Semiconductor (analog-to-digital converters) ADCs continue to make great progress and will likely nd applications in the SKA, but superconductor ADCs bene t from higher clock speeds and quantum accurate quantisation. We propose a superconducting softwarede ned radio frontend. The key component of such a frontend is a superconducting ash ADC. We show that employing such an ADC, even a small- to moderately-sized one, will signi cantly improve the instantaneous bandwidth observable by the SKA, yet retain adequate signal-to-noise ratio so as to achieve a net improvement in sensitivity. This improvement could approach factor 2 when compared to conventional technologies (at least for continuum observations). We analyse key components of such an ADC analytically, numerically and experimentally and conclude that fabrication of such an ADC for SKA purposes is certainly possible and useful. Simultaneously, we address the power requirements of high-performance computing (HPC). HPC on a hitherto unprecedented scale is a necessity for processing the vast raw data output of the SKA. Utilising the ultra-low-energy switching events of superconducting switches (certain Josephson junctions), we develop rst demonstrators of the promising eSFQ logic family, achieving experimentally veri ed shift-registers and deserialisers with sub-aJ/bit energy requirements. We also propose and show by simulation how to expand the applicability of the eSFQ design concept to arbitrary (unclocked) gates.
The two-dimensional finite element/boundary element method in electromagnetics : formulation, applications, error estimates and mesh adaptive procedures
(Stellenbosch : Stellenbosch University, 1994) Meyer, Frans J. C.(Frans Johannes Christiaan); Davidson, D. B.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
ENGLISH ABSTRACT: The Finite Element/Boundary Element (FE/BE) method is a numerical method which has been used successfully in the past few years to solve general electromagnetic problems. This thesis presents a general investigation of the two-dimensional FE/BE method for electromagnetic applications. The Finite Element Method (FEM) is formulated for application to 2D electromagnetic problems. It is shown that the FEM can be coupled to the Boundary Element Method (BEM), with the BEM serving as a Neumann boundary condition, on a boundary enclosing the FEM region. The formulation of the FE/BE method, as a special case of the FEM, is thus also presented. The implementation of the FE/BE method is considered. This involves the calculation of the matrix elements of a number of matrices associated with the FE/BE method as well as the solution of the FE/BE method matrix equation system. A priori solution time and memory requirement estimates for specified accuracies of FE/BE method solutions are also investigated. The 2D FE/BE method is applied to a number of electromagnetic problems for which analytical solutions exist. This serves as validation of the formulation and implementation of the FE/BE method. The 2D FE/BE method is then used to obtain approximated radar-cross section results as well as time domain pulse response results for elongated aerofoil shaped objects. The radar-cross section results are compared to measured results. The 2D FE/BE method is further used to model the effect of a human being on a man-pack radio antenna and vice versa. Electromagnetic radiation from 2D horn antennas, calculated with the 2D FE/BE method, is also considered. A number of a posteriori error estimates and error indicators for FE/BE method solutions of electromagnetic problems are formulated and developed. These include local (in each finite element) and global Element Residual Method (ERM) error estimates. L2 -norm boundary field and boundary field derivative error estimates, a L2 -norm Neumann boundary condition error indicator and radar width and radiation intensity error indicators. The implementation of these error estimates and error indicators is considered and it is shown that these implementation procedures result in highly efficient error estimates with negligible computational times. The a posteriori error estimates and error indicators developed are applied to a number of FEM and FE/BE method solutions of electromagnetic problems. These includes static electric field problems and electromagnetic scattering and radiation problems. The results obtained are used to investigate the accuracy, reliability and applicability of the different error estimates and error indicators when applied to FE/BE method solutions of general electromagnetic problems. Adaptive finite element methods and adaptive FE/BE methods are also considered. Adaptive procedures developed are applied to static electric field problems as well as electromagnetic scattering and radiation problems. Rates of convergence obtained with the adaptive methods are investigated. Conclusions are drawn regarding the work presented in this dissertation as well as further research that needs to be done on this topic.

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Browsing Doctoral Degrees (Electrical and Electronic Engineering) by browse.metadata.advisor "Davidson, D. B."

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