Solving the magnetostatic field problem (a case of high susceptibility) by means of the method of subsections

Abstract

A method is given for the numerical solution of the magnetostatic field problem of bodies with high susceptibility ( k > 1 SI). The surface integral equation of the problem is given. The integral equation is solved numerically by means of the method of subsections for two different geometries: 3-dimensional bodies whose boundaries are approximated by rectangular planes aligned with the coordinate planes, and 2 1 2 - dimensional bodies, where the cross-section of the boundaries are approximated by line segments oriented arbitrarily. Some numerical examples are considered. It is shown that the method of the demagnetization factor should not be used for the calculation of magnetostatic anomalies if the susceptibility of the model is higher than 1 SI. The demagnetization factors of a cube and a prism with axial ratios 1:1:2 are given for the susceptibility range 0.1–900 SI. It is shown that, for these models, the sum of the components of the demagnetization factor in the directions of its principal axes is approximately equal to unity when susceptibility is low (not more than 0.1 SI); when susceptibility equals 900 SI, however, the sum is reduced to 0.85.