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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.

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.

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.

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.

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 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.

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.

To circumvent the high computational costs of modelling each lamination to compute the eddy current distribution in three dimensions in conducting laminations, a simple method has been developed. The laminar nature of the eddy currents due to the magnetic leakage field has been considered by applying an anisotropic conductivity with zero or very low value in the direction normal to the laminations. This yields an overall field distribution serving as basis. In a second step, the much smaller eddy current loops caused by the main magnetic flux parallel to the laminations have been taken into consideration by a one‐dimensional analytical model. Nonlinearity is neglected.

The relation between the output of the fluxset sensor and the magnetic field is established by the numerical and experimental investigation of an ECT set‐up. A fast calculation method has been developed for obtaining the magnetic field generated by the interaction of the probe and the crack in a finite plate by superimposing the results obtained by the analysis of a finite plate without a crack and an infinite plate with a crack. The calculations are made by FEM and boundary integral methods, respectively. The relationship between the measured output and the magnetic field is obtained by calculating the calibration factors giving the best fit of the two sets of data. Based on the results, a numerical tool is developed for the quantitative evaluation of magnetic field sensors applied to the measurement of spatially inhomogeneous fields.

Perfectly matched layers (PMLs) are used for reflectionless truncation of the problem boundaries in finite element methods applications. In this paper, the method of PMLs is extended to truncate any lossless medium and the method is implemented for the T formulation.

The basic concept behind PMLs is to create an artificial material with a complex and diagonal anisotropic permittivity and permeability. For the A, V formulation PMLs are well known.

It is shown that it is possible to truncate any linear lossless material with PML layers, and if the material has small losses the PML works fine.

In the present paper, an artificial anisotropic lossy material is applied to a 3D edge finite‐element T, formulation to form perfectly matched layers.