A nonlinear eddy-current integral formulation for moving bodies

Abstract

This paper presents an integral formulation for the calculation of the eddy-current problems in moving conductors in the presence of magnetic media. The quasistationary Maxwell equations are written in local reference frames associated with moving bodies. Only the conducting and ferromagnetic domains are discretized. The eddy current is described in terms of a two component electric vector potential for which edge elements are used along with the tree-cotree decomposition. The magnetization is assumed to be uniform in each element of the ferromagnetic domain. Time stepping is used for time integration. The nonlinear problem is solved using Picard iteration, for which convergence is guaranteed. Only a part of the relevant matrices must be formed at each time step. The features of the method are illustrated with the aid of some numerical results

A Magnetic Flux–Electric Current Volume Integral Formulation Based on Facet Elements for Solving Electromagnetic Problems

“…A numerical solution can then be obtained by interpolating J and M, respectively, on c and m [5], [6]. However, other unknowns can be chosen: electric vector potential T (J = curl T) can be used in electric region [7], and magnetic scalar potential, for instance, can be used in magnetic region [8]. In this paper, we propose to use facet interpolations for J and B in conducting regions and magnetic regions, respectively.…”

Numerical solution of eddy current problems in ferromagnetic bodies travelling in a transverse magnetic field

“…Because of convergence problems caused by the velocity term in the case of high-speed upwind elements [10], moving co-ordinate systems [11] or a surface impedance method [12] were introduced. The possibility of including magnetic materials has been discussed by several authors using di erent methods [2,6,7].…”

“…Two main classes of methods were proposed for the computation of the electromagnetic ÿeld in conducting bodies moving through a magnetic ÿeld: di erential [2][3][4][5] and integral [6,7] formulations. Also, hybrid formulations appeared, e.g.…”

FEM/MOM formulation for the analysis of current distribution in rail launchers

“…The term S i v represents the relative velocity between the generic point on the i-th surface and the domain containing the source currents while k i v represents the relative velocity between points on the k-th and on the i-th surface. Discretization of the inner domains 1 Ω and 2 Ω , performed by means of tetrahedral elements results in a discretization of 1 S and 2 S by means of triangular elements.…”

“…Several computer codes based on both differential and integral formulation have been developed in the past years [1], [2]. Hybrid formulations combining both differential (typically FEM) and integral (typically MOM) formulations are under investigation as they seem promising in removing some drawbacks of both integral and differential formulations [3], [4], [6].…”