Volume integral equations in non‐linear 3‐D magnetostatics

In this paper a discussion of volume integral formulations in three‐dimensional non‐linear magnetostatics is presented. Integral formulations are examined in connection with Whitney's elements in order to find new approaches. A numerical algorithm based on a formulation implying properly the continuity conditions of magnetic field strength H, i.e. an h‐type formulation, is introduced. Results of demanding application problems are shown demonstrating the characteristics of this kind of volume integral approach. In addition, a discussion of the parallelized version of the numerical code based on the h‐type approach is presented appended with numerical results illustrating the advantages of combining integral formulations with concurrent computing.