Boundary element method for solution of 3-D magnetic fields

The boundary element method (BEM) has been established as an effective means for magnetostatic analysis. Direct BEM formulations for the magnetic vector potential have been developed over the past 20 years. There is a less well known direct boundary integral equation (BIE) for the magnetic flux density. On first inspection, the ancillary boundary integral equation for the magnetic flux density appears to be homogeneous, but it can be shown that the equation is well-posed and non-homogeneous using appropriate boundary conditions. In this paper we derive the BIE for the magnetic induction and show how it can be used to determine the surface fields on good conductors using an auxiliary constraint given by the integral form of Ampere's Law.