An investigation into direct sparse matrix solution schemes in the finite element method

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.

Grantor dc:publisher.institution

Department of Mechanical Engineering

Year dc:date.issued

1987

Author dc:creator

• Eastman, Michael Wayne

Advisor dc:contributor.advisor

• Vos, J

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/7603

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/7603