| This thesis explores the possibility of using the Boundary Integral Equation Method of minimum order to solve true three-dimensional eddy current problems, as a generalized approach. The BIE method of minimum order approach results in a set of singular equations, nevertheless, the degrees of freedom are minimized as the solution is obtained in terms of single scalar and single vector unknowns. In this thesis, simple schemes are presented to evaluate the singular integrals in the sense of Cauchy's principal value. For the first time, in the present work, the BIE method of minimum order is implemented to solve true three-dimensional eddy current problems.;Three classes of problems are solved using this method. First, an eddy current problem having smooth single connected surface in a time harmonic field is solved. The field variation and the power loss are compared with the available analytical solution. Second, the field distribution of a non-smooth single connected system in a time harmonic field is predicted. Finally, the BIE method of minimum order is generalized by extending it to solve a multiple connected system in the geometrical sense. A multiple connected system with the exterior field requirement is solved and the results are compared with the available experimental results.;It is known that the solution accuracy and the major computational requirement of the BIE method depends on the type of Gauss Integration methodology used. In this thesis, two Gauss integration schemes are presented to evaluate the singular and near singular integrals over the triangular patch along with the necessary mapping techniques and transformations. It is found that the irregular sub-triangulation scheme, proposed in this thesis, is highly suited to evaluate the near singular integrals due to the rapid rate of convergence and inherent computational advantages. However, the singular advantage of these integration schemes is the ease with which transformations can be incorporated in three-dimensional boundary element software. Furthermore, this thesis answers many questions on the implementation of the BIE method in solving three-dimensional problems. |
