Self-adaptive finite element analysis for three-dimensional magnetostatic systems
This thesis investigates the creation of a self-adaptive finite element analysis system, for three-dimensional magnetostatic problems. It uses as its basis the principle of complementary variations, adapted to apply to the relevant equation set. By making use of this principle, bounds can be placed on the accuracy of the solution to any given problem. The necessary three-dimensional standard and complementary magnetostatic functionals for this aim are rigorously developed. It is seen that the set of boundary conditions which may be used with the necessary formulations is restricted. The important task of automatic mesh generation is considered at some length. A survey of available techniques is made, and that most suited to the application under study is selected. A number of problems are highlighted, and the success of measures taken to correct them is established by experimentation. Numerous further tests are performed, to enable the performance of the chosen method to be quantified. Mesh refinement is tackled in a similar manner. A suitable method is chosen, and its performance is established by the undertaking of a series of realistic tests. The thesis concludes by examining the results of the application of the completed system to some trial problems.