Notes on boundary integral equations for three-dimensional magnetostatics

Several methods of formulating two-region magnetostatics problems with boundary integral equations and scalar potentials are discussed. These integral equations contain single- (i.e., monopole) and/or double- (i.e., dipole) layer source distributions. If only one type of source is used for both regions, certain numerical difficulties occur, which are discussed. For numerical accuracy a combined approach is adopted: it is sufficient to choose single layers in the exterior or less permeable region and to use double layers in the interior high-permeability region and at the interface. As an example, the combined method is applied to a recording head energized with a current loop.