Numerically efficient steady-state finite element analysis of magnetically saturated electromechanical devices using a shooting-Newton/GMRES approach

A numerically efficient steady-state finite element solver for electromechanical devices incorporating magnetic saturation is presented. The magnetization of ferromagnetic materials is modelled as a field-dependent equivalent current density. A Lagrangian representation of continuum variables is used, thereby removing numerical instabilities due to the Peclet effect but precluding the use of standard harmonic balance methods. The shooting-Newton method is therefore used to calculate the steady-state behavior. A matrix-free Krylov-subspace linear solver, the generalized minimum residuals method (GMRES), is shown to significantly reduce the computational burden by eliminating the need to calculate the shooting-Newton Jacobian. Simulation results from a synchronous reluctance motor model with 10288 nodes and 4935 elements confirm that the proposed method dramatically reduces computation time compared to running transient analysis until convergence.