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An investigation into direct sparse matrix solution schemes in the finite element method
Includes bibliographical references.
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| Main Author: | |
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Department of Mechanical Engineering
2014
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| _version_ | 1867614476824477696 |
|---|---|
| access_status_str | Open Access |
| author | Eastman, Michael Wayne |
| author2 | Vos, J |
| author_browse | Eastman, Michael Wayne Vos, J |
| author_facet | Vos, J Eastman, Michael Wayne |
| author_sort | Eastman, Michael Wayne |
| collection | Thesis |
| description | Includes bibliographical references. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/7603 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:52:39.496Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| publisher | Department of Mechanical Engineering |
| publisherStr | Department of Mechanical Engineering |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/7603 An investigation into direct sparse matrix solution schemes in the finite element method Eastman, Michael Wayne Vos, J Civil Engineering Includes bibliographical references. The application of the finite element method invariably involves the solution of large systems of sparse linear algebraic equations. The solution of these systems often represents a significant or even dominant component of the total solution time. Various sparse matrix techniques and strategies have been developed to reduce the time and cost of solving these equations. These techniques exploit both the zero-nonzero structure of the matrix problem and the manner in which the actual numerical components of the problem are computed. This thesis describes some of the direct methods, including the banded, sky line or profile, wavefront and hypermatrix schemes. The relative merits of each of these schemes are also indicated with respect to the number of arithmetical operations, data structure organization, secondary storage requirements and implementation strategy. The second section of this thesis discusses the implementation of an equation solution package for application in the finite element method. Initially a partitioning scheme for a wavefront solver was investigated but due to problems encountered and the increasing complexity of the code, it was decided to use an alternative method. A Cholesky decomposition method with a hypermatrix data storage scheme was then investigated and developed. The equation solution method was developed using a virtual paging scheme as implemented by the DAS package, and a module of general hypermatrix management routines. Finally, the package was implemented and tested in the NEW NOSTRUM development at the University of Cape Town. Suggestions for further developments are briefly discussed. 2014-09-22T07:54:43Z 2014-09-22T07:54:43Z 1987 Master Thesis Masters MSc http://hdl.handle.net/11427/7603 eng application/pdf Department of Mechanical Engineering Faculty of Engineering and the Built Environment University of Cape Town |
| spellingShingle | Civil Engineering Eastman, Michael Wayne An investigation into direct sparse matrix solution schemes in the finite element method |
| thesis_degree_str | Master's |
| title | An investigation into direct sparse matrix solution schemes in the finite element method |
| title_full | An investigation into direct sparse matrix solution schemes in the finite element method |
| title_fullStr | An investigation into direct sparse matrix solution schemes in the finite element method |
| title_full_unstemmed | An investigation into direct sparse matrix solution schemes in the finite element method |
| title_short | An investigation into direct sparse matrix solution schemes in the finite element method |
| title_sort | investigation into direct sparse matrix solution schemes in the finite element method |
| topic | Civil Engineering |
| url | http://hdl.handle.net/11427/7603 |
| work_keys_str_mv | AT eastmanmichaelwayne aninvestigationintodirectsparsematrixsolutionschemesinthefiniteelementmethod AT eastmanmichaelwayne investigationintodirectsparsematrixsolutionschemesinthefiniteelementmethod |