Thesis (MEng)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: The Method of Moments (MoM) is routinely used for the numerical solution of electromagnetic
surface integral equations. Solution errors are inherent to any numerical
computational method, and error estimators can be effectively employed to reduce and
control these errors. In this thesis, gradient recovery techniques of the Finite Element
Method (FEM) are formulated within the MoM context, in order to recover a higher-order
charge of a Rao-Wilton-Glisson (RWG) MoM solution. Furthermore, a new recovery procedure,
based specifically on the properties of the RWG basis functions, is introduced
by the author. These recovered charge distributions are used for a posteriori error estimation
of the charge. It was found that the newly proposed charge recovery method
has the highest accuracy of the considered recovery methods, and is the most suited for
applications within recovery based error estimation.
In addition to charge recovery, the possibility of recovery procedures for the MoM
solution current are also investigated. A technique is explored whereby a recovered charge
is used to find a higher-order divergent current representation. Two newly developed
methods for the subsequent recovery of the solenoidal current component, as contained in
the RWG solution current, are also introduced by the author. A posteriori error estimation
of the MoM current is accomplished through the use of the recovered current distributions.
A mixed second-order recovered current, based on a vector recovery procedure, was found
to produce the most accurate results.
The error estimation techniques developed in this thesis could be incorporated into an
adaptive solver scheme to optimise the solution accuracy relative to the computational
cost. / AFRIKAANSE OPSOMMING: Die Moment Metode (MoM) vind algemene toepassing in die numeriese oplossing van
elektromagnetiese oppervlak integraalvergelykings. Numeriese foute is inherent tot die
prosedure: foutberamingstegnieke is dus nodig om die betrokke foute te analiseer en te
reduseer. Gradiënt verhalingstegnieke van die Eindige Element Metode word in hierdie
tesis in die MoM konteks geformuleer. Hierdie tegnieke word ingespan om die oppervlaklading
van 'n Rao-Wilton-Glisson (RWG) MoM oplossing na 'n verbeterde hoër-orde
voorstelling te neem. Verder is 'n nuwe lading verhalingstegniek deur die outeur voorgestel
wat spesifiek op die eienskappe van die RWG basis funksies gebaseer is.
Die verhaalde ladingsverspreidings is geïmplementeer in a posteriori fout beraming
van die lading. Die nuut voorgestelde tegniek het die akkuraatste resultate gelewer, uit
die groep verhalingstegnieke wat ondersoek is.
Addisioneel tot ladingsverhaling, is die moontlikheid van MoM-stroom verhalingstegnieke
ook ondersoek. 'n Metode vir die verhaling van 'n hoër-orde divergente stroom
komponent, gebaseer op die verhaalde lading, is geïmplementeer. Verder is twee nuwe
metodes vir die verhaling van die solenodiale komponent van die RWG stroom deur die
outeur voorgestel. A posteriori foutberaming van die MoM-stroom is met behulp van die
verhaalde stroom verspreidings gerealiseer, en daar is gevind dat 'n gemengde tweede-orde
verhaalde stroom, gebaseer op 'n vektor metode, die beste resultate lewer.
Die foutberamingstegnieke wat in hierdie tesis ondersoek is, kan in 'n aanpasbare
skema opgeneem word om die akkuraatheid van 'n numeriese oplossing, relatief tot die
berekeningskoste, te optimeer.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/96881 |
| Date | 03 1900 |
| Creators | Strydom, Willem Jacobus |
| Contributors | Botha, Matthys M., Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | 103 page : illustrations |
| Rights | Stellenbosch University |
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