Browsing by Author "Steyn, Pierre"

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    Iterative methods in electromagnetic scattering based on the minimization of the root mean square error
    (Stellenbosch : Stellenbosch University, 1989) Steyn, Pierre; Davidson, D. B.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
    ENGLISH ABSTRACT: Iterative schemes based on the minimization of the error in scattering problems are presented. In particular, scattering by impenetrable objects is considered. These problems result in operator expressions of convolution type which are solvable using spectral methods. The numeric implementation involves the application of the discrete Fourier transform. A description of the computer implementation of these methods is followed by various numeric results which include a study of the rate of convergence of the schemes and the stability of the solution.
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    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.