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This work introduces an efficient and accurate technique to solve the eddy current problem in laminated iron cores considering vector hysteresis.

The mixed multiscale finite element method based on the based on the T,Φ-Φ formulation, with the current vector potential T and the magnetic scalar potential Φ allows the laminated core to be modelled as a single homogeneous block. This means that the individual sheets do not have to be resolved, which saves a lot of computing time and reduces the demands on the computer system enormously.

As a representative numerical example, a single-phase transformer with 4, 20 and 184 sheets is simulated with great success. The eddy current losses of the simulation using the standard finite element method and the simulation using the mixed multiscale finite element method agree very well and the required simulation time is tremendously reduced.

The vector Preisach model is used to account for vector hysteresis and is integrated into the mixed multiscale finite element method for the first time.

The aim of the present work is to find an efficient solution concerning the computational effort of quasi‐static electric field (QSEF) problems involving anisotropic conductivity and permittivity in the frequency domain.

Numerical simulations are carried out with tetrahedral nodal finite elements of first‐ and second‐order and with Withney elements. The solution of the boundary value problem with the aid of the electric scalar potential approximated by nodal finite elements is compared with those by the electric current vector potential represented by edge finite elements.

The simulation with an electric current vector potential approximated by the edge elements of first‐order prevail over that by the electric scalar potential approximated by nodal elements of second‐order concerning the memory requirements and the computation time at comparable accuracy.

The application of edge finite elements to solve QSEF problems considering an anisotropic complex conductivity in 3D.

The aim of the work is to reconstruct the anisotropic complex conductivity distribution with the common Gauss‐Newton algorithm.

A cubic region with anisotropic material properties is enclosed by a larger cube with isotropic material properties. Numerical simulations are done with tetrahedral nodal finite elements of second‐order.

It can be shown that it is possible to reconstruct anisotropic complex conductivity distribution if the starting values are chosen sufficiently close to the true values of the complex conductivity.

In this paper, the anisotropic electric conductivity and the anisotropic permittivity are reconstructed in 3D.

The simulation of eddy currents in laminated iron cores by the finite element method (FEM) is of great interest in the design of electrical devices. Modeling each laminate by finite elements leads to extremely large nonlinear systems of equations impossible to solve with present computer resources reasonably. The purpose of this study is to show that the multiscale finite element method (MSFEM) overcomes this difficulty.

A new MSFEM approach for eddy currents of laminated nonlinear iron cores in three dimensions based on the magnetic vector potential is presented. How to construct the MSFEM approach in principal is shown. The MSFEM with the Biot–Savart field in the frequency domain, a higher-order approach, the time stepping method and with the harmonic balance method are introduced and studied.

Various simulations demonstrate the feasibility, efficiency and versatility of the new MSFEM.

The novel MSFEM solves true three-dimensional eddy current problems in laminated iron cores taking into account of the edge effect.

Cables are ubiquitous in electronic-based systems. Electromagnetic emission of cables and crosstalk between wires is an important issue in electromagnetic compatibility and is to be minimized in the design phase. To facilitate the design, models of different complexity and accuracy, for instance, circuit models or finite element (FE) simulations, are used. The purpose of this study is to compare transmission line parameters obtained by measurements and simulations.

Transmission line parameters were determined by means of measurements in the frequency and time domain and by FE simulations in the frequency domain and compared. Finally, a Spice simulation with lumped elements was performed.

The determination of the effective permittivity of insulated wires seems to be a key issue in comparing measurements and simulations.

A space decomposition technique for a guided wave on an infinite configuration with constant cross-section has been introduced, where an analytic representation in the direction of propagation is used, and the transversal fields are approximated by FEs.

The purpose of this paper is an accurate computation of eddy currents in laminated media with minimal computer resources.

Modeling each laminate of the laminated core of electrical devices requires prohibitively many finite elements (FEs). To overcome this restriction a higher order multi-scale FE method with the magnetic vector potential

has been developed to cope with 3D problems considering edge effects.

The multi-scale FE approach facilitates an accurate simulation of the eddy current losses with minimal computer resources. Numerical simulations demonstrate a remarkable accuracy and low computational costs. The effect of regularization on the results is shown.

The eddy current losses are of great interest in the design of electrical devices with laminated cores.

The multi-scale FE approach takes also into account of the edge effects in 3D.

This paper aims to consider a multiscale electromagnetic wave problem for a housing with a ventilation grill. Using the standard finite element method to discretise the apertures leads to an unduly large number of unknowns. An efficient approach to simulate the multiple scales is introduced. The aim is to significantly reduce the computational costs.

A domain decomposition technique with upscaling is applied to cope with the different scales. The idea is to split the domain of computation into an exterior domain and multiple non-overlapping sub-domains. Each sub-domain represents a single aperture and uses the same finite element mesh. The identical mesh of the sub-domains is efficiently exploited by the hybrid discontinuous Galerkin method and a Schur complement which facilitates the transition from fine meshes in the sub-domains to a coarse mesh in the exterior domain. A coarse skeleton grid is used on the interface between the exterior domain and the individual sub-domains to avoid large dense blocks in the finite element discretisation matrix.

Applying a Schur complement to the identical discretisation of the sub-domains leads to a method that scales very well with respect to the number of apertures.

The error compared to the standard finite element method is negligible and the computational costs are significantly reduced.

The purpose of this paper is to study the extraction of scattering parameters (SPs) from simple structures on a printed circuit board (PCB) by the finite difference time domain (FDTD) method with the aid of a surface impedance boundary condition (SIBC).

The incorporation of SIBC into the FDTD method is described for the general case. The excitation of a field problem by a field pattern and the transition from the field solution to a circuit representation by SPs is discussed.

SPs obtained by FDTD with SIBC are validated with semi‐analytic solutions and compared with results obtained by different numerical methods. Results of a microstrip with a discontinuity considering losses are presented demonstrating the capability of the present method.

The comparison of numerical results obtained by different methods demonstrates the capability of the present method to extract SPs from PCBs very efficiently.

This paper aims to improve the efficiency of a numerical method to treat the eddy current problem on a laminated material, where using a mesh that resolves each individual laminate would be too computationally expensive.

The domain is modeled using a coarse mesh that treats the laminated material as a bulk with averaged properties. The fine-structured behavior is recovered by introducing micro-shape functions in the ansatz space. One such method is analyzed to find further model restrictions.

By using a special reformulation, it is possible to eliminate the additional degrees of freedom introduced by the multiscale ansatz at the cost of an additional modeling error that decreases with the laminate thickness.

The paper gives a computationally more efficient approximate variant to a known multiscale method.

The convergence of the transfinite‐element (TFE) method for high frequency methods is analyzed in this paper. Two different potential formulations will be compared in the frequency and time domain.

The A*‐and A,v‐formulation for time domain and frequency domain transfinite elements are described. The convergence properties of the methods are investigated and demonstrated on a simple test problem.

It is shown that the convergence of the frequency domain method depends also on the discretization of areas where the field values do not change very much. A numerical example shows that for the calculation of the whole frequency range, the time domain approach is much more faster than the frequency domain method.

Further, work should also cover additional formulations like, e.g. the T,Φ‐formulation.

Pros and cons of different formulations and methods for solving high frequency problems for printed circuit boards or microwave structures are investigated.

The originality of the paper is the comparison, the discussion and the explanations of the convergence of the TFE method for wave propagation.