A Domain Decomposition Method for Large-Scale 3-D Nonlinear Magnetostatic Problems

An iterative domain decomposition method is applied to numerical analysis of 3-dimensional (3-D) nonlinear magnetostatic problems taking the magnetic vector potential as an unknown function. The nonlinear simultaneous equations are solved with the Picard iteration or the Newton iteration. In Picard iteration, we compute the reluctivity using H-B curves, and in Newton iteration we compute the reluctivity using $ \ u-B $ curves or $ \ u-B^2 $ curves. The simultaneous linear equations at each step of the nonlinear iteration are solved by the iterative domain decomposition method. The iterative domain decomposition method is combined with the Conjugate Gradient (CG) procedure, and the Hierarchical Domain Decomposition Method (HDDM) which is adopted for the parallel computing. Numerical results show that the iterative procedure converges, and that the computed magnetic flux density is suitable