THEORETICAL FORMULATION OF A TIME-DOMAIN FINITE ELEMENT METHOD FOR NONLINEAR MAGNETIC PROBLEMS IN THREE DIMENSIONS (Invited Paper)

Abstract

Abstract-In this work, a numerical solution of nonlinear ferromagnetic problems is formulated using the three-dimensional time-domain finite element method (TDFEM) combined with the inverse JilesAtherton (J-A) vector hysteresis model. After a brief introduction of the J-A constitutive model, the second-order nonlinear partial differential equation (PDE) is constructed through the magnetic vector potential in the time domain, which is then discretized by employing the Newmark-β scheme, and solved by applying the Newton-Raphson method. Different Newton-Raphson schemes are constructed and compared. The capability of the proposed methods is demonstrated by several numerical examples including the simulation of the physical demagnetization process, the prediction of the magnetic remanence in the ferromagnetic material, and the generation of higher-order harmonics.

NUMERICAL STUDY OF A TIME-DOMAIN FINITE ELEMENT METHOD FOR NONLINEAR MAGNETIC PROBLEMS IN THREE DIMENSIONS (Invited Paper)

“…In this section, we briefly review the nonlinear inverse J-A hysteresis model [6] and the TDFEM formulation for nonlinear magnetic problems developed in [1], and present simple numerical examples for validation.…”

“…Such a nonlinear system can be solved iteratively by using the polarization technique and the Newton-Raphson method as [1] [J]{δa} = −{r} (12)…”

“…in which H is obtained from the J-A model presented in Section 2.1, and ν opt r is a constant, which can be chosen as [1] With the definition of ν opt r , the stiffness matrix [S p ] can be calculated as…”

“…In our previous work [1], a numerical solution to the nonlinear magnetic problem is formulated with a three-dimensional time-domain finite element method (TDFEM) [2] combining with the inverse vector Jiles-Atherton (J-A) model [3][4][5][6]. The physical problem is expressed as a nonlinear second-order partial differential equation (PDE) in the time domain, which is solved using the Newton-Raphson or Newtonlike methods.…”

Time Decomposition Method for the General Transient Simulation of Low-Frequency Electromagnetics

“…This choice allows engineers to analyze the dynamic system including the nonlinear materials, permanent magnets and induced eddy currents under a variety of conditions, under various excitations including the pulsed waveform. This procedure is usually very time-consuming since it requires N t · N e matrix solutions, where N t is the number of time steps and N e is the average number of nonlinear iterations [1][2][3][4][5][6]. Provided that an algorithm (or method) can be made parallel, parallel computing can cut down simulation time for a nonlinear transient problem.…”