A Magnetic Vector Potential Volume Integral Formulation for Nonlinear Magnetostatic Problems

Abstract

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.

A semi-analytical method to compute the magnetic flux linkage of a 2D meshed coil in presence of magnetic materials − application to electrical motor pre-design

“…This coupling allows to gather good quality results rather quickly compared to the Finite Element Method. We can see that in addition to being as precise as the FEM for normally meshed problems [7,8,17] is very efficient in a predesign context, which was the aim of this study.…”

An Integral Face Formulation for Thin Non-Conductive Magnetic Regions

“…In previous papers, it has been proposed to solve (4) choosing B as unknown [1] or even the magnetic vector potential [2]. However, these formulations were limited to volume magnetic regions and their use in the context of magnetic shielding is not efficient in terms of computation time.…”

“…A magnetostatic integral method based on first order facet elements interpolation of the magnetic flux density has already been proposed in [1]. A very similar formulation based on the edge interpolation of the magnetic vector potential can also be found in [2]. Unfortunately, both approaches have been developed for volume regions and cannot be simply applied to thin shell geometry because the thickness has to be meshed, leading to a huge number of elements.…”

“…7. Let us notice that to take into account T-shape geometry is easy with B-formulation presented here but not natural with vector potential formulation [2].…”

An expression of the magnetic co-energy adapted to magnetostatic volume integral formulations - application to the magnetic force computation

“…For a few years, Volume Integral Method (VIM) has been widely studied [4] [1][2] [3] and is know today as a good alternative to the Finite Elements Method (FEM) for solving magnetostatic problems in the presence of non-linear materials. While the FEM needs the geometry to be completely meshed, the VIM only requires the meshing of active materials.…”