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The purpose of this paper is to present a time domain discontinuous Galerkin (DG) approach for modeling wideband frequency dependent surface impedance boundary conditions.

The paper solves the Maxwellian initial value problem in a computational domain, which is spatially discretized by the higher order DG method. On the boundary of the computational domain the paper applies a suitable impedance boundary condition (IBC). The frequency dependency of the impedance function is modeled by auxiliary differential equations (ADE).

The authors will study the resonance frequency and the Q factor of different types of cavity resonators including lossy materials. The lossy materials are modeled by means of IBCs. The authors will compare the results with analytical results, as well as numerical results obtained by direct calculations where lossy materials are included explicitly into the numerical model. Several convergence studies are performed which demonstrate the accuracy of the approach.

Modeling of frequency dependent boundary conditions in time domain with finite difference time domain method (FDTD) method is considered in numerous papers, as well as in frequency domain finite element method (FEM), and in a few papers also time domain FEM. However, FDTD method is only first order accurate and fails in modeling of complicated surfaces. FEM allows for high order accuracy, but time domain modeling is numerically extremely expensive. In frequency domain, broadband modeling of frequency dependent boundary conditions requires several simulations as opposed to the time domain, where a single simulation is needed. The time domain DG method proposed in this paper allows to overcome the difficulties. The authors introduce a broadband surface impedance formulation based on the ADE approach for the higher order DG method.

To show a possible implementation of surface impedance boundary conditions (SIBCs) in a time domain formulation based on the cell method (CM).

The implementation is based on vector fitting (VF), a technique which allows a time domain representation of a rational approximation of the surface impedance to be found.

It is shown that very little computational effort is needed to find a very good VF approximation of simple SIBCs and that such approximation is easily fitted into existing CM codes.

The extension to higher order SIBCs has not been taken into account.

The proposed approach avoids the use of convolution integrals, is accurate and easy to implement.

This paper introduces the use of VF for the approximate time domain representation of SIBCs.

The purpose of this paper is the derivation and efficient implementation of surface impedance boundary conditions (SIBCs) for nonlinear magnetic conductors.

An approach based on perturbation theory is proposed, which expands to nonlinear problems the methods already developed by the authors for linear problems. Differently from the linear case, for which the analytical solution of the diffusion equation in the semi-infinite space for the magnetic field is available, in the nonlinear case the corresponding nonlinear diffusion equation must be solved numerically. To this aim, a suitable smooth map is defined to reduce the semi-infinite computational domain to a finite one; then the diffusion equation is solved by a Galerkin method relying on basis functions constructed via the push-forward of a Lagrangian polynomial basis whose degrees of freedom are collocated at Gauss–Lobatto nodes. The use of such basis in connection with a suitable under-integration naturally leads to mass-lumping without impacting the order of the method. The solution of the diffusion equation is coupled with a boundary element method formulation for the case of parallel magnetic conductors in terms of E and B fields.

The results are validated by comparison with full nonlinear finite element method simulations showing very good accordance at a much lower computational cost.

Limitations of the method are those arising from perturbation theory: the introduced small parameter must be much less than one. This implies that the penetration depth of the magnetic field into the magnetic and conductive media must be much smaller than the characteristic size of the conductor.

The efficient implementation of a nonlinear SIBC based on a perturbation approach is proposed for an electric and magnetic field formulation of the two-dimensional problem of current driven parallel solid conductors.

The aim of this paper is to propose a design procedure based on the impedance boundary condition in order to simplify the design of inductors for domestic induction heating systems.

An electromagnetic description of the inductor system is performed to substitute the effects of a component, named system load, for a mathematical condition, the so‐called impedance boundary condition. This is suitable to be used in electromagnetic systems involving high conductive materials at medium frequencies, as it occurs in an induction heating system. Applying this approach, a simplified electrical model arises from the general system.

A considerable reduction in the efforts devoted to design a coil for induction heating purposes is achieved, because the solution considering the variation of three physical parameters are projected to a one‐dimensional space only depending on a single parameter named corrected penetration depth. This proposal assesses the working conditions of standard induction systems.

This work is performed to achieve a better understanding of the fundamentals involved in the electromagnetic modeling of an induction heating system. The main goal is the definition of a better coil design process because it is probably the most time‐consuming task in the construction of a complete induction system.

In this paper, the so‐called corrected penetration depth is defined. This single parameter allows explaining the influence of the physical parameter of the inductor load and the excitation frequency in the equivalent of the complete inductor system. The numerical results carried out considering the corrected penetration depth instead of the physical load properties have been validated experimentally.

The purpose of this paper is to propose an approach based on Convolution quadrature (CQ) for the modeling and the numerical treatment of impedance boundary condition.

The model is derived from a general setting. Its discretization is discussed in details by providing pseudo-codes and by performing their complexity analysis. The model is validated through several numerical experiments.

CQ provides an efficient and accurate treatment of impedance boundary conditions.

The paper suggests a new effective treatment of impedance boundary conditions.

This paper aims to present a lightened 3D finite element model (FEM) for coupled electromagnetic thermal simulation of the induction thermography non-destructive testing (NDT) technique to reduce the computation time.

The time harmonic electromagnetic problem is expressed in A – ϕ formulation and lightened by using the surface impedance boundary condition (SIBC) applied to both the massive induction coil surface and the surface of conductor workpiece including open cracks. The external circuit is taken into account by using the impressed voltage or the impressed current formulation. The thermal diffusion in the workpiece is solved by using surface electromagnetic power density as thermal source.

The accuracy and the usefulness of the method for the design of the induction thermography NDT technique have been shown with acceptable deviation compared with a full FEM model. It is also observed that at high frequency, when the ratio between the local radius of the conductor and the skin depth is high, a very good accuracy can be obtained with the SIBC methods. At lower frequency, the effect of the curvature of the surface becomes significant. In this case, the use of the Mitzner’s impedance can help to correct the error.

The SIBC can be used for both massive coil and workpieces with open cracks to alleviate 3D FEMs of the coupled electrothermal model. The implementation in matrix form of the coupled electrothermal formulation is given in details. The comparisons with reference analytical solution and full 3D FEM show the accuracy and performance of the method. In the test case presented, the computation time is 6.6 times lower than the classical model.

This paper aims to study unstructured-partial element equivalent circuit (PEEC) method for modelling electromagnetic regions with surface impedance condition (SIBC) is proposed. Two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The formulation is applied in the context of low frequency problems with volumic magnetic media and coils. Non simply connected regions are treated with fundamental branch independent loop matrices coming from the circuit representation.

Because of the use of Whitney face elements, two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The air is not meshed.

The new surface impedance formulation enables the modeling of volume conductive regions to efficiently simulate various devices with only a surface mesh.

The propagation effects are not taken into account in the proposed formulation.

The formulation is original and is efficient for modeling non simply connected conductive regions with the use of SIBC. The unstructured PEEC SIBC formulation has been validated in presence of volume magnetic nonconductive region and compared with a SIBC FEM approach. The computational effort is considerably reduced in comparison with volume approaches.

To provide a time domain formulation for reconstruction of transient currents flowing in massive parallel conductors from magnetic data collected in the dielectric space surrounding the conductors.

A boundary integral equation (BIE) formulation involving Mitzner's and Rytov's high order surface impedance boundary conditions (SIBCs) is used. Input data of the inverse problem are the magnetic fields at given locations near the conductors. In order to validate the inversion algorithm, the magnetic field data are computed solving the direct problem with FEM for given current waveforms.

The improvement in reconstruction accuracy of the new time domain BIE formulation employing high order SIBCs has been demonstrated numerically in a simple test case. The range of validity of the technique has been extended to current pulses of longer duration and the computational burden has shown to increase only by a factor of 4.

The proposed formulation can be compared with other possible formulations, both in the time and in the frequency domain.

Based on this formulation a new current sensing technique is proposed for realization of low cost current sensors based on magnetic sensor arrays.

The inverse problem addressed in the paper has been solved for the first time.

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.

The purpose of this paper is to offer a simulation method for predicting the impedance of machine windings at higher frequencies.

A transmission‐line model (TLM) is developed based on parameters calculated on the basis of electroquasistatic and magnetoquasistatic finite‐element (FE) model of the winding cross‐section.

The FE formulations for the low‐ and high‐frequency limits give acceptable results for the respective frequency ranges. An eddy‐current formulation is only accurate on a broader region when the FE mesh is sufficiently fine to resolve the skin depth.

The paper is restricted to frequency‐domain simulations.

The results of the paper improve the understanding of higher‐frequency parasitic effects in electrical drives with long windings.

The paper shows the limitations of the FE methods used for determining the parameters of the TLMs and remedies to avoid these.