A volume integral formulation for nonlinear magnetostatics and eddy currents using edge elements

The properties of Whitney elements provide the basis of a novel integral formulation for solving three-dimensional magnetostatics and eddy-current problems. Using a tree structure reduces the number of unknowns to a few less than the number of nodes for the static case, a significant saving over earlier integral formulations. Interface conditions are satisfied exactly, but the material constitutive relations are satisfied only approximately. The resulting magnetostatics code, GFUNET, is attractive in terms of convenience, CPU time utilization, and accuracy. It realizes much of the speedup promised by parallel computing. Results for an accelerator sextupole magnet and for TEAM Workshop problem Hash 13 are presented.>