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The purpose of this study is to determine the steady state of an electromagnetic structure using the finite element method (FEM) without calculation of the transient state. The proposed method permits to reduce the computation time if the transient state is important.

In the case of coupling magnetic and electric circuit equations to obtain the steady state with periodic conditions, an approach can be to discretise the time with periodic conditions and to solve the equation system. Unfortunately, the computation time can be prohibitive. In this paper, the authors proposed to use the waveform relaxation method associated with the Newton method to accelerate the convergence.

The obtained results show that the proposed approach is efficient if the transient state is important. On the contrary, if the transient state is very low, it is preferable to use the classical approach, namely, the time-stepping FEM.

The main limitation of the proposed approach is the necessity to evaluate or to know the time constant and consequently the duration of the transient state. Moreover the method requires some important memory resources.

In the context of the use of the time-stepping FEM, one of the problems is the computation time which can be important to obtain the steady state. The proposed method permits avoidance of this difficulty and directly gives the steady state.

The proposed approach will permit to model and study the electromagnetic systems in the steady state, and particularly the transformers. Because of the gain in computing time, the use of optimisation techniques will be facilitated.

The novelty of this study is the proposal of the waveform relaxation–Newton method to directly obtain the steady state when applied to the three-phase transformer.

To extend the field application of numerical simulation, it is necessary in many applications to consider the electric circuit. Usually the magnetic equations are solved using the 3D finite element method which implies the solution of a non‐linear equations system. To solve the electric circuit equations a mesh or a state variable method can be used. It may be noted that the electric equation system obtained with these methods can also be non‐linear in presence of semi‐conductor components in the electric circuit. If the interaction between the magnetic and electric circuits is important both non‐linear matrix systems must be solved simultaneously.

To compare the numerical solutions in primal and dual meshes of magnetostatic problems solved with the finite integration technique.

The development of the whole set of magnetostatic discrete formulations is proposed. Four formulations are computed: two in terms of fields and two in terms of potentials. Moreover, each computation is carried out on the primal and dual mesh. Two applications are presented and the results are analysed and discussed.

The whole set of magnetostatic formulations gives only two solutions. The solutions do not depend of the formulation, but they depend of the choice of the field discretisation in primal or dual mesh.

The computation is carried out on the dual mesh.

This paper presents a method of coupling magnetostatic potential formulations with electrical circuits for the 3D FEM. Allowing for the current density distribution in stranded conductors, two vectors N and K are introduced. A systematic method of decomposing both vectors in Whitney’s element spaces is suggested. This method can be used for coils with a complex shape. As an example of application a three‐phase transformer is studied.

In this communication, the Preisach and Jiles‐Atherton models are studied to take hysteresis phenomenon into account in finite element analysis. First, the models and their identification procedure are briefly developed. Then, their implementation in the finite element code is presented. Finally, their performances are compared with an electromagnetic system made of soft magnetic composite. Current and iron losses are calculated and compared with the experimental results.

To compare slip surface and moving band techniques for modelling movement in 3D with FEM.

The slip surface and moving band techniques are used to model the rotation of electrical machines in 3D with FEM. The proposed techniques are applied to a permanent magnet synchronous machine. The comparison is carried out at no‐load for the electromotive force (EMF) and the cogging torque. The torque is also compared for the short circuit case.

For both the locked‐step and moving band approaches there is no difficulty in establishing the scalar potential and potential vector formulations. However, if step displacement is not equal to the mesh step, the results can show numerical irregularities. Some improvements have been proposed in order to limit this problem.

The results of the EMF and the cogging torque are improved.

The aim of this work is to present the details of the finite element approach that was developed for solving the Landau‐Lifschitz‐Gilbert (LLG) equations in order to be able to treat problems involving complex geometries.

There are several possibilities to solve the complex LLG equations numerically. The method is based on a Galerkin‐type finite element approach. The authors start with the dynamic LLG equations, the associated boundary condition and the constraint on the magnetization norm. They derive the weak form required by the finite element method. This weak form is afterwards integrated on the domain of calculus.

The authors compared the results obtained with our finite element approach with the ones obtained by a finite difference method. The results being in very good agreement, it can be stated that the approach is well adapted for 2D micromagnetic systems.

The future work implies the generalization of the method to 3D systems. To optimize the approach spatial transformations for the treatment of the magnetostatic problem will be implemented.

The paper presents a special way of solving the LLG equations. The time integration a backward Euler method has been used, the time derivative being calculated as a function of the solutions at times n and n+1. The presence of the constraint on the magnetization norm induced a special two‐step procedure for the calculation of the magnetization at instant n+1.

To provide an approach to design the optimal open type magnetic circuit of permanent magnet producing uniform field.

The Biot‐Savart's law and evolution strategy are used for the initial design of permanent magnet configuration. In order to improve the uniformity, the ON/OFF method, which is the topology optimization method, is used for determining the shape of magnetic material which is set around the permanent magnet.

The optimal topology of permanent magnet and shape of magnetic material around it, which can produce nearly uniform field of about 0.15T, is obtained. The obtained uniformity is 3,583 ppm. More work for improving the uniformity is necessary.

A new approach for obtaining the optimal shape of open type magnetic circuit which may be used for magnetic resonance imaging is carried out.

The purpose of this paper is to compare torque calculation methods when a non‐conforming movement interface is implemented by means of Lagrange multipliers.

The following methods are here used for computing the torque in a synchronous machine and in a switched reluctance motor: Arkkio's method (AM), local Jacobian matrix derivative (LJD) method, Maxwell stress tensor method (MST) and co‐energy variation method.

This paper shows that, the numerical stability produced by Lagrange multipliers yields a stable torque result, even in thin airgap machines if AM, LJD method or MST method are used.

This work presents a comparative study to indicate the performance of the most commonly used torque calculation methods, when a non‐conforming technique is used, considering a small displacement of the rotor, which is necessary for dynamic cases or coupling with circuit.