Differentiation algorithms for soft magnetic material models

Anisotropic soft materials are fully described by mapping the stored energy or coenergy density over the space of flux density or magnetic field components. This method requires accurate numerical differentiation and reliable data. Two algorithms are described. One is fast and suitable for starting Newton iterations. The other is more costly, but yields accurate second derivatives. Current laboratory techniques are sufficiently accurate, but measurements must be spread over the coordinate space so that numerous points lie in the multidimensional knee region of the material.