A Magnetic Vector Potential Volume Integral Formulation for Nonlinear Magnetostatic Problems

Vinh Le Van (1) , Gérard Meunier (1) , Olivier Chadebec (1) , Jean-Michel Guichon (1)

1 G2ELab - Laboratoire de Génie Electrique de Grenoble

treated straightforwardly, and the nonlinear problems convergence was easily reached without any relaxation technique. Nevertheless, the B-facet formulation requires independent loops search in order to restore the flux solenoidality. This task can be time consuming and decreases the convergence rate of linear systems solutions. In this paper, an original magnetostatic volume integral formulation based on the interpolation of the magnetic vector potential on edge elements is proposed. This novel approach, called A-edge formulation, does not require the independent loops search algorithms. The formulation being auto-gauged, no gauge condition has to be added and the convergence rate of the linear solution is then improved. In others words, this new formulation has all the benefits of the B-facet one but without its drawbacks. II. MAGNETIC VECTOR POTENTIAL FORMULATION Let us consider a 3-D magnetostatic problem composed by ferromagnetic regions and coils with DC current density J. We note the boundary between and the free space. Volume integral method (VIM) has been known as an interesting alternative to the finite-element method for electromagnetic field computation. Since only the active regions have to be meshed, VIM is very efficient for modeling of electromagnetic devices containing a predominated air volume. It is also adapted for multistatic studies with motion or optimization strategies. The aim of this paper is to propose a magnetic vector potential volume integral formulation in order to deal with the 3-D nonlinear magnetostatic problems. The main advantage of this formulation is that the convergence of nonlinear material solution can be easily reached after a few iterations without any relaxation. Moreover, the use of coarse meshes can lead to accurate results. Computed results for the TEAM Workshop problem 13 and for an actuator are reported.

Mots clés: Edge elements; integral equation; magnetic vector potential; nonlinear magnetostatic; team Workshop problem 13; volume integral method.

Domaines: Energie électrique

Vinh Le Van, Gérard Meunier, Olivier Chadebec, Jean-Michel Guichon. A Magnetic Vector Potential Volume Integral Formulation for Nonlinear Magnetostatic Problems. IEEE Transactions on Magnetics, 2016, 52 (3), ⟨10.1109/TMAG.2015.2490627⟩. ⟨hal-01385525⟩