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# Hybrid Finite Element/Boundary Element solutions of general two dimensional electromagnetic scattering problems

Meyer, Frans J. C. (Frans Johannes Christiaan) (1991-02)

Thesis (MEng) -- University of Stellenbosch, 1991.

Thesis

ENGLISH ABSTRACT: A two-dimensional Coupled Element Method (CEM) for solving electromagnetic scattering problems involving lossy, inhomogeneous, arbitrarily shaped cylinders, was investigated and implemented. The CEM uses the Finite Element Method (FEM) to approximate the fields in and around the scatterer and the Boundary Element Method (BEM) to approximate the far-field values. The basic CEM theory is explained using the special, static electric field problem involving the solution of Laplace's equation. This theory is expanded to incorporate scattering problems, involving the solution of the Helmholtz equation. This is done for linear as well as quadratic elements. Some of the important algorithms used to implement the CEM theory are discussed. Analytical solutions for a round, homogeneous- and one layer coated PC cylinder are discussed and obtained. The materials used in these analytical solutions can be lossy as well as chiral. The CEM is validated by comparing near- and far-field results to the analytical solution. A comparison between linear and quadratic elements is also made. The theory of the CEM is further expanded to incorporate scattering from chiral media

AFRIKAANSE OPSOMMING: 'n Gekoppelde Element Metode (GEM) wat elektromagnetiese weerkaatsingsprobleme, van verlieserige, nie-homogene, arbitrere voorwerpe kan oplos, is ondersoek en geimplimenteer. Die GEM gebruik die Eindige Element Metode (EEM) om die velde in en om die voorwerp te benader. 'n Grenselementmetode word gebruik om die vervelde te benader. Die basiese teorie van die GEM word verduidelik deur die toepassing daarvan op die spesiale geval van 'n statiese elektriese veld- probleem. Hierdie probleem verlang die oplossing van Laplace se vergelyking. Die teorie word uitgebrei om weerkaatsingsprobleme te kan hanteer. Die weerkaatsingsprobleme verlang die oplossing van 'n Helmholtz-vergelyking. Hierdie teorie word ontwikkel vir lineere sowel as kwadratiese elemente. Van die belangrike algoritmes wat gebruik is om die GEM-teorie te implimenteer, word bespreek. Analietise oplossings vir ronde, homogene en eenlaag bedekte perfek geleidende silinders word bespreek en verkry. Die material wat in die oplossings gebruik word, kan verlieserig of kiraal wees. Die GEM word bekragtig deur naby- en verveld resultate te vergelyk met ooreenkomstige aitalitiese oplossings. Die lineere en kwadratiese element- resultate word ook met mekaar vergelyk. Die GEM-teorie is verder uitgebrei sodat weerkaatsing vanaf kirale materiale ook hanteer kan word.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/69271

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