Iterative FEM-BEM technique for an efficient computation of magnetic fields in regions with ferromagnetic bodies

Inside the ferromagnetic bodies the magnetic field is determined by applying the Finite Element Method (FEM) with a Dirichlet boundary condition for the magnetic potential. The resulting tangential component of the field intensity is used as boundary condition for the exterior field problem whose solution is obtained by the Boundary Element Method (BEM) which provides the new boundary condition for the interior problem. The nonlinearity of the highly permeable ferromagnetic material is treated by implementing the Polarization Fixed Point Method (PFPM), where the magnetic polarization is corrected in terms of the field intensity. While preserving the intrinsic advantages of the FEM and the BEM, separately, the proposed technique also allows to easily take into consideration the terminal voltage of the coils as input data and a simple field solution for multiply connected structures, such as transformers, electrical machines, and a multitude of electromagnetic devices.