Comparison of different boundary integral formulations when coupled with finite elements in three dimensions

Several boundary integral formulations are described and compared for calculating the `outside stiffness matrix¿¿ for a hybrid finite-element boundary-integral method in three-dimensional (3D) electromagnetic modelling. The methods of single-layer sources and of Green´s identity, as well as the Trefftz method, have been analysed when using, respectively, collocation and variational techniques for the numerical discretisation. The analysis shows that results obtained by both of the Green´s identity and the single-layer methods are similar, and that the Trefftz method can be seen as a special case of the latter method. In other respects, as the single-layer method is more convenient in exterior field calculation, it has been adopted by the authors. The choice of the source distribution and the treatment of singularities by using a semi-analytical technique or by locating the virtual sources separated from the boundary are also discussed. The different methods have been numerically implemented in the `Trifou¿¿ (3D eddy-current computation) code. Calculations for a test example, concerning eddy currents in a hollow sphere, have been completed. The obtained results have been compared and the corresponding conclusions are given at the end of the paper.