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The purpose of this paper is to use different model order reduction techniques to cope with the computational effort of solving large systems of equations. By appropriate decomposition of the electromagnetic field problem, the number of degrees of freedom (DOF) can be efficiently reduced. In this contribution, the Proper Generalized Decomposition (PGD) and the Proper Orthogonal Decomposition (POD) are used in the frame of the T-Ω-formulation, and the feasibility is elaborated.

The POD and the PGD are two methods to reduce the model order. Particularly in the context of eddy current problems, conventional time-stepping algorithms can lead to many numerical simulations of the studied problem. To simulate the transient field, the T-Ω-formulation is used which couples the magnetic scalar potential and the electric vector potential. In this paper, both methods are studied on an academic example of an induction furnace in terms of accuracy and computational effort.

Using the proposed reduction techniques significantly reduces the DOF and subsequently the computational effort. Further, the feasibility of the combination of both methods with the T-Ω-formulation is given, and a fundamental step toward fast simulation of eddy current problems is shown.

In this paper, the PGD is combined for the first time with the T-Ω-formulation. The application of the PGD and POD and the following comparison illustrate the great potential of these techniques in combination with the T-Ω-formulation in context of eddy current problems.

The purpose of this paper is to propose some a posteriori residual error estimators (REEs)to evaluate the accuracy of the finite element method for quasi-static electromagnetic problems with mixed boundary conditions. Both classical magnetodynamic A-ϕ and T-Ω formulations in harmonic case are analysed. As an example of application the estimated error maps of an electromagnetic system are studied. At last, a remeshing process is done according to the estimated error maps.

The paper proposes to analyze the efficiency of numerical REEs in the case of magnetodynamic harmonic formulations. The deal is to determine the areas where it is necessary to improve the mesh. Moreover the error estimators are applied for structures with mixed boundary conditions.

The studied application shows the possibilities of the residual error estimators in the case of electromagnetic structures. The comparison of the remeshed show the improvement of the obtained solution when the authors compare with a reference one.

The paper provides some interesting results in the case of magnetodynamic harmonic formulations in terms of potentials. Both classical formulations are studied.

The paper provides some informations to develop the proposed formulations in the software using finite element method.

The paper deals with the possibility to improve the determination of the meshes in the analysis of electromagnetic structure with the finite element method. The proposed method can be a good solution to obtain an optimal mesh for a given numerical error.

The paper proposes some elements of solution for the numerical analysis of electromagnetic structures. More particularly the results can be used to determine the good meshes of the finite element method.

The calculation of electromagnetic fields can involve many degrees of freedom (DOFs) to achieve accurate results. The DOFs are directly related to the computational effort of the simulation. The effort is decreased by using the proper generalized decomposition (PGD) and proper orthogonalized decomposition (POD). The purpose of this study is to combine the advantages of both methods. Therefore, a hybrid enrichment strategy is proposed and applied to different electromagnetic formulations.

The POD is an a-priori method, which exploits the solution space by decomposing reference solutions of the field problem. The disadvantage of this method is given by the unknown number of solutions necessary to reconstruct an accurate field representation. The PGD is an a-priori approach, which does not rely on reference solutions, but require much more computational effort than the POD. A hybrid enrichment strategy is proposed, based on building a small POD model and using it as a starting point of the PGD enrichment process.

The hybrid enrichment process is able to accurately approximate the reference system with a smaller computational effort compared to POD and PGD models. The hybrid enrichment process can be combined with the magneto-dynamic T-Ω formulation and the magnetic vector potential formulation to solve eddy current or non-linear problems.

The PGD enrichment process is improved by exploiting a POD. A linear eddy current problem and a non-linear electrical machine simulation are analyzed in terms of accuracy and computational effort. Further the PGD-AV formulation is derived and compared to the PGD-T-Ω reduced order model.

Coreplates in large generators may suffer from local short circuits. An accurate analysis is required to avoid these failures and detect them when occurring. The purpose of this paper is to develop a lamination stack model compliant with interlamination default analysis.

An electromagnetic model should account for the eddy‐current in the lamination stack. To avoid the modelling of the insulation between the steel sheets, the authors propose to introduce a condition on the fields applied between each sheet. In the case of electric fault between several sheets, the conducting domain, i.e. the sheets, is not simply connected. Then, T‐Ω formulation must be adapted to solve such problem.

The model allows to account for thin plates, insulating layers and electrical faults in electromagnetic modeling of core plates. This study leads to a first evaluation of eddy current losses in steel laminations with defaults.

The present study does not take into account thermal effects. The next step will consist in a magneto‐thermal computation. Thus, an electromagnetic finite element software must be coupled with a thermal one. An other improvement will rely on the study of actual situation in order to evaluate the accuracy of industrial sensors and to compare with measurements.

The paper develops a lamination stack model compliant with interlamination default analysis. As far as the authors know, this is the first study on 3D electromagnetic modeling.

Benchmark problem 10 of the TEAM workshop consists of steel plates around a coil (non‐linear transient eddy current problem). Seven computer codes are applied, and seven solutions are compared with each other and with experimental results.

To provide a selective bibliography for researchers and graduate students who have an interest in induction processes applied to the electromagnetic processing of materials.

The objective is to provide references that identify seminal, early work, and references that represent the current state of the art. References are listed in categories that cover the broad range of induction modeling and application issues.

A brief overview of the key areas in induction processing of materials is provided, but greater emphasis and space is devoted to the references provided.

The middle years of each topic area are not covered.

A very comprehensive coverage of material is provided to those with an interest in induction processing of materials.

This paper fulfils an identified information/resources need.

We present a method for the simulation of the dynamical behavior of a coupled magneto‐mechanical system given in terms of a conductor moving through an electromagnetic field.

For the magnetic part, we consider a model based on an electric vector and a magnetic scalar potential, whereas the mechanical part is modelled by the equation of a rigid body motion. A weak coupling is employed: at each time step the resulting forces are calculated yielding the new displacement of the conductor.

Numerical results are given for the simulation of an electromagnetic brake with axisymmetric geometry. They indicate that the proposed method is especially well suited for eddy current problems involving moving conductors.

Further research should be undertaken toward the application of the proposed method to real 3D problems.

The spatial discretization of the problem relies on the use of two independent triangulations to approximate the two involved potentials. Whereas the scalar magnetic potential is discretized by means of nodal H¹‐conforming finite elements on a grid covering the global computational domain, the vector electric potential is approximated by H^curl‐conforming edge elements on another grid only covering the conductor. The coupling between the two grids is accomplished via the mortar finite element method. At each time step, only the coupling matrix has to be reassembled, all other involved matrices remain the same. Moreover, no remeshing is necessary when the conductor changes its position. The paper should be valuable for any researcher interested in the numerical simulation of eddy current problems.

The classical ϕ‐a formulations for numerical dosimetry of currents induced by extremely low frequency magnetic fields requires that the source field is provided through a vector potential. The purpose of this paper is to present a new formulation t‐b which directly takes the flux density as source term.

This formulation is implemented through finite element and validated by comparison with analytical solutions. The results obtained by both formulations are compared in the case of an anatomical computational phantom exposed to a vertical uniform field.

A good agreement between the t‐b formulation and both numerical and analytical computations was found.

This new formulation seems to be more accurate than the ϕ‐a formulation, and is more suited for situations where the magnetic field is known from experimental measurements, as there is no need for a magnetic vector potential.

Saturated core type superconducting fault current limiter (SFCL) can effectively limit the short-circuit current in power system. However, the high induced voltage will occur between the terminals of DC superconducting bias winding caused by the variation of magnetic flux linked by DC winding due to the increasing short-circuit current. The DC source may be damaged. Thus, the induced voltage should be considered in DC winding design. The paper aims to discuss these issues.

Three-dimensional finite element method coupled with electric circuit.

The short-circuit current flowing through AC windings and induced voltage of DC winding are analyzed by using three-dimensional finite element method coupled with electric circuit for a 220-kV three-phase SFCL. Several circuit elements, such as a capacitor connected with DC winding in parallel, an additional short-circuit winding wound around DC core column and an energy-released piezoresistor, are, respectively, used for induced voltage reduction. These methods aim to save magnetic coupled energy in DC winding, or oppose the variation of magnetic flux, or limit the voltage of DC winding by using a resistor with low resistance.

The different methods for reduction of induced voltage of superconducting DC winding are studied and discussed. The decreased induced voltage may benefit the safety of superconducting DC winding and the source.

The electromagnetic fields have a great influence on the behaviour of all the living systems. The as low as reasonably achievable (ALARA) principle imposes, in case of long exposures to low (i.e. power systems) or high frequency (i.e. microwave systems or cell phones) fields, some limitations to the radiated fields by the industrial equipment. On the other hand, some benefits can be taken from the effects of the electromagnetic fields on the living being: the hyperthermal technique is well known for the treatment of the cancer. Either we want to be protected from the fields, or we want to take benefit of the positive effects of these fields, all the effects thermal as well as genetic have to be well known. Like in any industrial application, the electromagnetic field computation allows a better knowledge of the phenomena, and an optimised design. Hence, there is a very important challenge for the techniques of computation of electromagnetic fields. The major difficulties that appear are: (1) related to the material properties – the “material” (the human body) has very unusual properties (magnetic permeability, electric permittivity, electric conductivity), these properties are not well known and depend on the activity of the person, and this material is an active material at the cell scale; (2) related to the coupling phenomena – the problem is actually a coupled problem: the thermal effect is one of the major effects and it is affected by the blood circulation; (3) related to the geometry – the geometry is complex and one has to take into account the environment. The problems that we have to face with are – the identification of the properties of the “material”, the coupled problem solution and the representation of the simulated phenomena.