A Volume Integral Formulation Based on Facet Elements for Nonlinear Magnetostatic Problems

Abstract

This paper presents a novel and useful 3D nonlinear magnetostatic integral formulation for volume integral method. Like every other integral formulation, its main advantage is that it does not require air region mesh, only ferromagnetic regions being discretized. The formulation is based on magnetic flux density interpolation on facet elements. Special care is taken in order to accurately compute the singularity of Green's kernel. The application of an equivalent circuit approach allows preserving the solenoidality of magnetic induction. It is shown that the formulation is very accurate even if it is associated with coarse meshes. Thus, computation time can be very competitive. Computed results for the TEAM Workshop problem 13 and for a multiply-connected regions case-test 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.…”

“…While the FEM needs the whole geometry to be meshed (air, active materials, sources etc…), the volume integral method (VIM) only requires the meshing of active materials. For a few years, the VIM has been widely studied [6][7][8] and is know today as a good alternative to the FEM for solving magnetostatic problems in the presence of non-linear materials thanks to the robust acceleration method for its resolution. The magnetic field in the magnetic materials will thus be computed thanks to a 2D VIM presented in [9].…”

An Integral Face Formulation for Thin Non-Conductive Magnetic Regions

“…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].…”

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.…”