A hybrid method using BEM and FDM for the calculation of 2-D magnetic fields including materials with field-dependent permeability

The use of the boundary element method (BEM) for the calculation of magnetic fields (M. Strِer, Optik 77 (1987) 15; R. Becker, Nucl. Instr. and Meth. B 42 (1989) 303; A 298 (1990) 13) has distinct advantages, like high accuracy, no problems with open boundaries and numerically smooth solutions, which are essential for paraxial particle optics analysis. However, it is impossible to take into account the nonlinear properties of iron cores. In this paper we present the extension of INTMAG (Becker, 1989, 1990) to a hybrid computer program by applying the finite difference method to the iron volume (Weth, Dissertation FB Physik, Universitنt Frankfurt/Main 1997), while using BEM to determine the currents at the iron surface, in order to satisfy there the refraction laws for the magnetic field. The volume currents are determined to represent the curl of the magnetisation, divided by the local and field-dependent permeability. Examples will be given for the convergence behaviour of this method and for the resulting distribution of volume currents. A comparison is also made with measurements, showing the success of this hybrid method.