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The divergence equations in Maxwell’s theory are Gauss law and the statement that magnetic monopoles do not exist; from this point of view these two equations are fundamental. However, from a practical point of view, it is generally believed that Maxwell’s divergence equations are redundant and may be ignored provided that they are satisfied at some time t‐0. It has been proved recently that this idea is not correct for boundary‐initial value problems. To make mathematical arguments more accessible, we analyse here the role of the divergence equations in the framework of 2D‐electromagnetism.

A new finite volume scheme to solve Maxwell’s equations is presented. The approach is based on a leapfrog time scheme and a centered flux formula. This method is well suited for handling complex geometries, and therefore we can use unstructured grids. It is also able to capture the discontinuities of the electromagnetic fields through different media, without producing spurious oscillations. Owing to these properties, we can treat difficult problems, such a computing a scattered wave across complex objects. An analysis of the scheme is presented and numerical experiments are performed.

The paper aims at proposing a uniform and demonstrative description of two well‐known and widely used approximations of slowly time‐varying electromagnetic fields, i.e. the electro‐quasistatic and the magneto‐quasistationary approximation to Maxwell's equations.

Under both approximations, the orders of magnitude of the relative errors of the dominant fields are analyzed by using three characteristic time constants. These time constants are determined by considering the material properties, the characteristic length scale and the characteristic time scale.

Limiting curves which show the domains of applicability of the two approximations are retrieved from the estimation of their relative errors. The relation between the domains of validity of the electro‐quasistatic and magneto‐quasistationary approximations was found and depicted in a combined diagram.

The study is restricted to slowly time‐varying electromagnetic fields. Heuristic and local estimates based on local material properties were used for the analysis. Rigorous estimations of the errors (e.g. also considering the field problem's topology) of the magneto‐quasistationary approximation are already known in the literature. A rigorous estimation of the error of the electro‐quasistatic approximation is, therefore, suggested for future research.

The combined diagram showing the domains of validity of both approximations considered here in a uniform way is novel. It gives rise to an intuitive and easily accessible understanding of their applicability.

In this paper, special attention is focused on the study of the relaxation phenomena of fabrics containing elastane yarn.

For this purpose, the relaxation phenomena of wound fabric under constant deformation, as the consequence of accumulated stress during winding, were analysed. Maxwell's model and the modified standard linear solid model are used for explaining the relaxation.

The results of the study of the relaxation phenomena of fabrics containing elastane yarn show a close connection between stress relaxation under constant deformation in the fabric roll and the degree of deformation with manual unwinding. Expert knowledge of the relaxation phenomena in fabrics containing elastane yarns has a big influence on explaining the problem of dimensional changes and instability in such fabrics.

A better understanding of the relaxation phenomena in fabrics containing elastane yarns.

This paper aims to present a modified precise integration time domain (PITD) method for the numerical solution of 2D scalar wave equation.

The split step (SS) scheme is applied to factorize the conventional PITD calculation into two sub-steps procedures and then field components can be updated along one spatial direction only in each sub-step. The perfectly matched layer (PML) absorber is extended to this method for modeling open region problems by using the stretched coordinate approach.

It is shown that this method requires less computation time and storage space in comparison with the conventional PITD method, yet maintains the numerical stability despite using large time steps.

The WE-PITD method requires the divergence free region, which may be a limit on its usage. Hence, there is a challenge of using this technique in the 3D problems.

Based on the SS scheme, the PITD method is used to solve the scale wave equation rather than Maxwell's equations, leading to a significant reduction in the computation time and memory usage.

The purpose of this paper is to provide a brief introduction of the finite difference based parabolic equation (PE) modeling to the advanced engineering students and academic researchers.

A three-dimensional parabolic equation (3DPE) model is developed from the ground up for modeling wave propagation in the tunnel via a rectangular waveguide structure. A discussion of vector wave equations from Maxwell’s equations followed by the paraxial approximations and finite difference implementation is presented for the beginners. The obtained simulation results are compared with the analytical solution.

It is shown that the alternating direction implicit finite difference method (FDM) is more efficient in terms of accuracy, computational time and memory than the explicit FDM. The reader interested in maximum details of individual contributions such as the latest achievements in PE modeling until 2021, basic PE derivation, PE formulation’s approximations, finite difference discretization and implementation of 3DPE, can learn from this paper.

For the purpose of this paper, a simple 3DPE formulation is presented. For simplicity, a rectangular waveguide structure is discretized with the finite difference approach as a design problem. Future work could use the PE based FDM to study the possibility of utilization of meteorological techniques, including the effects of backward traveling waves as well as making comparisons with the experimental data.

The proposed work is directly applicable to typical problems in the field of tunnel propagation modeling for both national commercial and military applications.

This paper aims to propose a semianalytical model of a squirrel-cage induction machine (SCIM), considering local magnetic saturation and eddy-currents induced in the rotor bars.

The regions of the rotor and stator are divided into elementary subdomains (E-SDs) characterized by general solutions at the first harmonic of the magneto-harmonic Maxwell’s equations. These E-SDs are connected in both directions (i.e., along the r- and θ-edges).

The calculation of the magnetic field has been validated for various values of slip and iron permeability. All electromagnetic quantities were compared with those obtained using a two-dimensional finite-element method. The semianalytical results are satisfactory compared with the numerical results, considering both the amplitude and waveform.

Expansion of the recent analytical model (E-SD technique) for the full prediction of the magnetic field in SCIMs, considering the local saturation effect and the eddy-currents induced in the rotor bars.

The purpose of this paper is to propose an efficient numerical simulation tool based on FEM, by which the EMC shielding effect characteristics of power cables can be predicted in the 30-1,000 MHz frequency range, as if it would be measured by the absorbing clamp method.

The simulation method is based on decomposition: a 2D axisymmetric RF FE model is used for describing the whole measurement set-up, while a 3D quasi-static FE model is used for the symmetry cell of the shielding layer in order to capture the effect of its fine geometric details.

Comparison with real measurements shows that the shielding characteristics can be reliably predicted this way, with some deviation in the low end of the frequency range though.

This simulation tool can be applied in the design and optimization of braided cable shields to be used in the automotive industry.

Two numerical models are coupled by the novel concept of “equivalent shielding layer”, which is obtained by homogenization.

The purpose of this paper is to present a 3D finite element model of the electromagnetic fields in an AC three‐phase electric arc furnace (EAF). The model includes the electrodes, arcs, and molten bath.

The electromagnetic field in terms of time in AC arc is also modeled, utilizing a 3D finite element method (3D FEM). The arc is supposed to be an electro‐thermal unit with electrical power as input and thermal power as output. The average Joule power, calculated during the transient electromagnetic analysis of the AC arc furnace, can be used as a thermal source for the thermal analysis of the inner part of furnace. Then, by attention to different mechanisms of heat transfer in the furnace (convection and radiation from arc to bath, radiation from arc to the inner part of furnace and radiation from the bath to the sidewall and roof panel of the furnace), the temperature distribution in different parts of the furnace is calculated. The thermal model consists of the roof and sidewall panels, electrodes, bath, refractory, and arc. The thermal problem is solved in the steady state for the furnace without slag and with different depths of slag.

Current density, voltage and magnetic field intensity in the arcs, molten bath and electrodes are predicted as a result of applying the three‐phase AC voltages to the EAF. The temperature distribution in different parts of the furnace is also evaluated as a result of the electromagnetic field analysis.

This paper considers an ideal condition for the AC arc. Non‐linearity of the arc during the melting, which leads to power quality disturbances, is not considered. In most prior researches on the electrical arc furnace, a non‐linear circuit model is usually used for calculation of power quality phenomena distributions. In this paper, the FEM is used instead of non‐linear circuits, and calculated voltage and current densities in the linear arc model. The FEM results directly depend on the physical properties considered for the arc.

Steady‐state arc shapes, based on the Bowman model, are used to calculate and evaluate the geometry of the arc in a real and practical three‐phase AC arc furnace. A new approach to modeling AC arcs is developed, assuming that the instantaneous geometry of the AC arc at any time is constant and is similar to the geometry of a DC arc with the root mean square value of the current waveform of the AC arc. A time‐stepping 3D FEM is utilized to calculate the electromagnetic field in the AC arc as a function of time.

Designers of electrical machines need a clear understanding of the mechanism of noise generation, in order to be able to reduce the noises which are produced under the influence of forces due to the magnetic field. The purpose of this paper is to develop a new approach to give a best estimation of these forces.

A model is developed to calculate the distribution of local forces using the virtual work principle in finite element context including ferromagnetic hysteresis. The forces are calculated using a formulation based on the energy derivation. The nonlinear behaviour of ferromagnetic material is considered by combining a Jiles‐Atherton model and finite element method through the fixed‐point iterative technique.

The effects of accurate behaviour of magnetic material are not always taken into account when calculating the local forces in electromagnetic devices. The introduction of hysteresis phenomenon in the analysed device gives a good prediction of magnetic induction. The expression used to compute the force includes an integral which is estimated numerically and not a constant term.

The developed approach is more accurate than the classical methods using constant magnetic permeability or a first magnetization curve.