Conference Agenda

An adaptive mesh refinement procedure is presented in order to address efficiently low frequencies electromagnetic problems with the unstructured inductive PEEC method. An a posteriori error estimator based on an equilibrated energy criterion and on a method of calculating a second admissible solution are proposed. TEAM Workshop problem no7 has been treated in order to show the good efficiency of the procedure.

To deal with magnetic problem at finite temperature, hybrid Monte Carlo (HMC) micromagnetics method has been proposed in the past years. Previous study of HMC micromagnetics is based on finite difference mesh (FDM), FDM usually consists of identical micromagnetic cells, the fast Fourier transformation (FFT) algorithm can be applied to speed up the simulation, but FDM has difficulty in dealing with irregular shaped model. To overcome the geometry difficulty encountered in FDM, the finite element mesh (FEM) based HMC micromagnetics method is developed in this work. For the ellipsoidal shaped single domain magnetic particle, the decrease of coercive field versus temperature can be explained by FEM-HMC micromagnetics, and the numerical results agree well with analytical ones. The FEM-HMC micromagnetics method could be a useful tool in dealing with magnetic problem with irregular shape at finite temperature, it has promising application in the study of engineering device.

In this paper, the Parareal algorithm is proposed for the parallelization of the time-periodic finite-element method (TPFEM) in nonlinear magnetic field analysis of transformers. This algorithm divides the entire time period into several sub-intervals and then performs calculations simultaneously in each sub-interval, which can effectively deal with the electromagnetic field calculation problem under a large time period. The Parareal TPFEM is applied to analyze the nonlinear magnetic characteristics of transformers with subsynchronous components, and numerical results show a high convergence speed.

The numerical simulation in time domain analysis of electromagnetic field problems often suffers the high computational burden due to the huge time discretization steps. In our previous work, Sinc interpolation method has been applied to time-domain solution of dynamic electromagnetic problems to reduce this computation burden. However, to construct Sinc interpolation, a huge matrix system is still needed to be solved in the pretreatment phase. To address this issue, we propose to apply the proper orthogonal decomposition (POD) to reduce the order of the corresponding matrix system in the Sinc method. Meanwhile, an energy defined norm is introduced in the POD process. It is observed that with this norm, the relative error between the reduced model and the full model can be improved.

The analysis of multi-degrees of freedom motion in electromagnetic field is usually subjected to huge computational burden due to the mesh deformation. In this paper, a new method combining Euler and Lagrange approaches is proposed to analyze the stability of a magnetic levitation system. The electromagnetic-mechanical coupling can be considered efficiently by the proposed method avoiding the time-consuming re-meshing. Besides, a stability model describing the damping coefficient of the motion system is proposed to provide guidance for the system stability design.

In this communication, the Normal Form (NF) method is employed to solve a 1D nonlinear magnetodynamic problem. The discrete model is formulated in a state-space form fit for NF applications. The resulting system is then expanded on a linear mode basis to cubic order. Analytical solutions are obtained using the NF technique and compared to time stepping solutions. The results show the cubic polynomial adequately approximates the problem, and the NF solution is valid for some range of magnetic field intensity.

In order to reduce the computational time induced by solving a finite element (FE) model for a magnetostatic problem with varying geometric parameters, a parametric geometric metamodel is defined using the Proper Generalized Decomposition (PGD) approach. The mesh deformation associated with the geometric variation is implemented using the Radial Basis Functions (RBF) interpolation method. The proposed approach is applied to a device composed of a magnetic circuit with a moving part. The results show that the PGD metamodel can accurately approximate the FE solution, for the cases of one and two coupled geometric parameters.

This paper introduces the truncation errors and round-off errors in the numerical differential calculation of magnetic field. To calculate the critical step size at different order, the index of peak position deviation is proposed, and the possible range and probability distribution of the two kinds of errors at each order are described, and the index of peak position deviation is derived, which can be used to calculate the critical step size of the derivative of the magnetic field of the grounding grid at a certain order.

The parallelization efficiency of the new iterative solver which name is k-skip Mister R (MrR) for the linear system obtained from the edge element is numerically investigated. In the electromagnetic analysis, the finite element method (FEM) with an edge element is often adopted as discretizing procedure, and a large sparse linear system with a rank deficient coefficient matrix is derived by the method. In order to obtain a specific solution of the system, Krylov subspace method is adopted as the solver. In the present study, we select MrR as a candidate solver for the linear system. In addition, we apply an algorithm to the method to avoid collective communication, which causes degradation of parallelization efficiency and verifies its effectiveness numerically.

In this work, a mixed domain decomposition method (LATIN) is proposed to improve the efficiency of magnetostatic simulation of rotating machines. This strategy relies on a decomposed formulation of the problem considering both primal and dual fields on the interfaces. From this formulation, the LATIN solver method gives a powerful iterative scheme to build a solution. A first implementation using the potential vector formulation in 2D is developped and is illustrated on two test cases: a ferromagnetic 2D bar and a switched reluctance motor.

A H-matrix-based preconditioner is applied to a symmetric linear-system solver in the shielding current analysis of a HTS film. In addition, its performance is investigated numerically. The results of computations show that the number of iterations for proposed method is much shorter than that for the conjugate gradient method. On the other hand, speedup ratio increases with the number of nodes. From the above results, H-matrix-based preconditioner is useful to the improvement of the solver speed for a large-scale simulation.

In this paper, we investigate the modeling of high temperature superconductors characterized with constitutive power law. The nonlinear vectorial problem obtained from Maxwell's equations is solved with a finite element method. To deal with the convergence problems due to the power law, a linearization method is applied. This linearization consists in a first order approximation of E(J) relation using a Jacobian matrix. However, in several cases the computations are slows because each time step requires a substancial number of iterations of the Newton method. By modifying the Jacobian matrix, it is possible to reduce this number of iterations and thus save the computation time.

An inductance calculation method of a soft magnetic composite (SMC) inductor considering the anisotropic magnetic characteristics due to compression molding is proposed. First, a particle model with a flattened iron particle and a uniform layer of insulation is constructed to represent the anisotropic BH curves in arbitrary directions by using the limited two BH curves under the compression application to longitudinal and lateral directions. Then, the dc-biased characteristic of permeability is introduced into the proposed particle model. Moreover, the proposed method is applied to two inductors with legs having different compress directions. It is shown that the anisotropic magnetic characteristics should be considered to calculate the inductance accurately and the proposed method can almost represent the dc-biased characteristic of inductance obtained from the measurement.

Vibration and noise become the important factors that restrict the development of transformers and motors to large capacity. The most effective method to restrain their vibration and noise is to fix the cores with clamps and shells. However, the compressive stress from clamps and shells will make the magnetic domains deflect in the same direction, that is the stress-induced anisotropy, which affects the degree of magnetization and magnetostriction of the material. Thus, the appropriate compressive stress will change the magnetic domain orientation of the core material, resulting in less magnetostriction under magnetic field excitation and reducing the vibration of the device. This paper proposed a free energy model of silicon steel based on the principle of minimizing magnetic domain energy. The model can simulate the deflection path of the magnetic domain under external magnetic field and stress by calculating the distribution of the energy extreme point. According to the magnetic and stress-induced anisotropy of silicon steel, the best value of external magnetic field strength and compressive stress is selected, which will provide a theoretical basis for designing low noise core structure of transformers and motors.

The electric field computation in composite materials induces a huge number of degrees of freedom and consequently a long computation time. In order to save the computation time and keep local information at the microscopic scale, model order reduction methods can be applied. In this context, the proper orthogonal decomposition is applied and a first comparison is made between the results of a model order reduction method and the results of the global voltammetry test.