Browsing by Author "Hansmann, Riana Helena"

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    2D Edge-based finite elements for guided and scattered wave problems
    (Stellenbosch : Stellenbosch University, 1999-03) Hansmann, Riana Helena; Davidson, D. B.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
    ENGLISH ABSTRACT: This thesis may be divided into two parts: the first describes the Finite Element Method (FEM) and its application to guided wave problems. The second part is devoted to scattering configurations, specifically the use of the Boundary Element Method (BEM) and the hybrid Finite Element Method-Boundary Element Method (FEM-BEM) to obtain solutions for scattering problems. The formulations are restricted to two dimensions throughout the thesis. A variational formulation is introduced and the implementation of boundary conditions is described. The use of vector approximation functions for the Finite Element Method is explained and the advantages highlighted. The properties of these functions are derived and graphical representations are given. A comparison between a lower order and higher order approximation is made. This is applied to problems which demonstrate the capabilities of the Finite Element Method such as ridged waveguides and circular waveguides containing eccentric dielectric rods. Results obtained compare well to analytic solutions, in the cases where these are available. An integral equation for scattering problems is derived. This relates the tangential field components on a contour enclosing a scattering object to the scattered fields and enables a solution to be obtained when the tangential components on the contour are known. It is shown how the interior region enclosed by the contour is discretised and how the Finite Element Method can be coupled with the Boundary Element Method by imposing continuity conditions on the enclosing contour. The resulting system of equations obtained may be solved. Solutions for scattering from perfectly conducting cylinders are obtained and compare well to analytic results.