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Electromagnetic field solutions via the finite element method
This thesis examines the application of the finite element method to the solution of two important equations which govern electromagnetic fields, namely, the Poisson equation and the Helmholtz equation. These equations. together with appropriate boundary conditions, describe boundary value and eigen...
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| Format: | Thesis |
| Language: | Eng |
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Department of Electrical Engineering
2016
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| _version_ | 1867614029366689792 |
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| access_status_str | Open Access |
| author | Watkins, L R |
| author2 | Reddy, B Daya |
| author_browse | Reddy, B Daya Watkins, L R |
| author_facet | Reddy, B Daya Watkins, L R |
| author_sort | Watkins, L R |
| collection | Thesis |
| description | This thesis examines the application of the finite element method to the solution of two important equations which govern electromagnetic fields, namely, the Poisson equation and the Helmholtz equation. These equations. together with appropriate boundary conditions, describe boundary value and eigenvalue problems respectively. Attention will be restricted to boundary value and eigenvalue problems on domains in R² in which more than one dielectric medium may be present. Weak or variational statements of these problems are derived, comprising the governing partial differential equation and appropriate boundary conditions. The Galerkin method is used to pose the variational statement of the problem in a finite-dimensional subspace and the finite element method employed to generate an appropriate set of basis functions which spans this subspace. A linear matrix or linear matrix eigenvalue problem results and suitable techniques for their numerical solution are presented. Various corrputat ional aspects of the finite element method and the solution techniques are discussed. Finite element programs capable of running on a microcomputer are developed and are used to analyse a number of electromagnetic field problems. The results of these analyses are compared, where possible, with analytic solutions, and elsewhere with results obtained by other methods. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/21964 |
| institution | University of Cape Town (South Africa) |
| language | Eng |
| last_indexed | 2026-06-10T12:45:32.767Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Electrical Engineering |
| publisherStr | Department of Electrical Engineering |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/21964 Electromagnetic field solutions via the finite element method Watkins, L R Reddy, B Daya Electrical Engineering This thesis examines the application of the finite element method to the solution of two important equations which govern electromagnetic fields, namely, the Poisson equation and the Helmholtz equation. These equations. together with appropriate boundary conditions, describe boundary value and eigenvalue problems respectively. Attention will be restricted to boundary value and eigenvalue problems on domains in R² in which more than one dielectric medium may be present. Weak or variational statements of these problems are derived, comprising the governing partial differential equation and appropriate boundary conditions. The Galerkin method is used to pose the variational statement of the problem in a finite-dimensional subspace and the finite element method employed to generate an appropriate set of basis functions which spans this subspace. A linear matrix or linear matrix eigenvalue problem results and suitable techniques for their numerical solution are presented. Various corrputat ional aspects of the finite element method and the solution techniques are discussed. Finite element programs capable of running on a microcomputer are developed and are used to analyse a number of electromagnetic field problems. The results of these analyses are compared, where possible, with analytic solutions, and elsewhere with results obtained by other methods. 2016-09-28T18:58:29Z 2016-09-28T18:58:29Z 1986 Master Thesis Masters MSc (Eng) http://hdl.handle.net/11427/21964 Eng application/pdf Department of Electrical Engineering Faculty of Engineering and the Built Environment University of Cape Town |
| spellingShingle | Electrical Engineering Watkins, L R Electromagnetic field solutions via the finite element method |
| thesis_degree_str | Master's |
| title | Electromagnetic field solutions via the finite element method |
| title_full | Electromagnetic field solutions via the finite element method |
| title_fullStr | Electromagnetic field solutions via the finite element method |
| title_full_unstemmed | Electromagnetic field solutions via the finite element method |
| title_short | Electromagnetic field solutions via the finite element method |
| title_sort | electromagnetic field solutions via the finite element method |
| topic | Electrical Engineering |
| url | http://hdl.handle.net/11427/21964 |
| work_keys_str_mv | AT watkinslr electromagneticfieldsolutionsviathefiniteelementmethod |