The two-dimensional finite element/boundary element method in electromagnetics : formulation, applications, error estimates and mesh adaptive procedures

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dc.contributor.advisorDavidson, D. B.en_ZA
dc.contributor.authorMeyer, Frans J. C.(Frans Johannes Christiaan)en_ZA
dc.contributor.otherStellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.en_ZA
dc.date.accessioned2012-08-27T11:39:03Zen_ZA
dc.date.available2012-08-27T11:39:03Zen_ZA
dc.date.issued1994en_ZA
dc.descriptionDissertation (Ph. D.) -- University of Stellenbosch, 1994.en_ZA
dc.description.abstractENGLISH 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.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING: Die Eindige Element/Grens Element (EE/GE) metode is 'n numeriese metode wat die afgelope paar jaar suksesvol aangewend is om algemene elektromagnetiese probleme op te los. 'n Algemene ondersoek van die twee-dimensionele (2D) EE/GE-metode vir elektromagnetiese toepassings word in hierdie tesis aangebied. Die Eindige Element Metode (EEM) word geformuleer vir 2D elektromagnetiese toepassings. Daar word getoon dat die Grens Element Metode (GEM) aangewend kan word as 'n spesiale Neumann randvoorwaarde op 'n grens wat die EEM gebied omisluit. Die EE/GE-metode, as 'n spesiale geval van die EEM, word dus ook geformuleer. Die implementering van die EE/GE-metode word ondersoek. Dit behels die berekening van matrikselemente van 'n aantal matrikse (wat geassosieer word met die EE/GE-metode) asook die oplossing van die matriksvergelykings van die EE/GE-metode. A priori oplossings tyd en geheue beramers vir spesifieke akkuraathede van EE/GE-metode oplossings word ook ondersoek. Die 2D EE/GE-metode word aangewend om 'n paar elektromagnetiese probleme op te los waarvoor daar analitiese oplossings bestaan. Dit dien as 'n verifiëring van die korrekte formulering en implementering van die EE/GE-metode. Die 2D EE/GE-metode word dan aangewend om benaderde radardeursnit-resultate asook tydgebied-pulsweergawe-resultate vir langwerpige draagvlak gevormde voorwerpe te verkry. Die radardeursnit-resultate word vergelyk met gemete resultate. Die 2D EE/GE-metode word verder aangewend om die effek van die menslike liggaam op 'n man-pak antenna, en omgekeerd, te modelleer. Elektromagnetiese stralings van 2D horingantennas, bereken met die 2D EE/GE-metode, word ook ondersoek. 'n Aantal a posteriori foutberamers en foutindikators vir EE/GE-metode oplossings van elektromagnetiese problerne word geformuleer en ontwikkel. Dit sluit in lokale (in elke eindige element) en globale Element Residu Metode (ERM) foutberamers, L2 -norm grensveld en grensveld afgeleide foutberamers, 'n L2 -norm Neumann randvoorwaarde foutindikator en radarwydte en stralingsintensiteit foutindikators. Die implementering van die foutberamers en foutindikators word ondersoek en daar word getoon dat hierdie implementeringsmetodes gebruik kan word om hoogs effektiewe foutberamers, met weglaatbare berekeningstye, te verkry. Die a posteriori foutberamers en foutindikators wat ontwikkel is, word toegepas op 'n paar EEM en EE/GE-metode oplossings van elektromagnetiese probleme. Dit sluit in statiese elektriese probleme en elektromagnetiese weerkaatsings- en stralingsprobleme. Die resultate wat verkry word, word gebruik om die akkuraatheid, betroubaarheid en toepaslikheid van die verskillende foutberamers en foutindikators te ondersoek. Aanpasbare eindige element metodes en aanpasbare EE/GE metodes word ook ondersoek. Aanpasbare prosedures wat ontwikkel is word toegepas op statiese elektriese probleme asook elektromagnetiese weerkaatsings- en stralingsprobleme. Die tempo van konvergensie wat verkry word met die aanpasbare metodes word ondersoek. Gevolgtrekkings word gemaak in verband met die werk wat in die tesis aangebied word asook verdere navorsing wat in die gebied gedoen kan word.af_ZA
dc.description.versionDoctoralen_ZA
dc.format.extent310 pages : illustrationsen_ZA
dc.identifier.urihttp://hdl.handle.net/10019.1/58617en_ZA
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch Universityen_ZA
dc.subject.lcshFinite element methoden_ZA
dc.subject.lcshElectromagnetism -- Mathematicsen_ZA
dc.subject.lcshElectromagnetic waves -- Mathematicsen_ZA
dc.subject.lcshElectromagnetic waves -- Scattering -- Mathematicsen_ZA
dc.subject.lcshBoundary element methodsen_ZA
dc.subject.lcshDissertations -- Engineeringen_ZA
dc.titleThe two-dimensional finite element/boundary element method in electromagnetics : formulation, applications, error estimates and mesh adaptive proceduresen_ZA
dc.typeThesisen_ZA
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