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Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The impedance boundary condition is widely used in order to reduce a multiple region electromagnetic field problem to a magnetic field problem analyzed in a nonconducting region only. It is obvious that the solution to the latter problem is much easier to obtain than those for conducting regions. There are several versions of the impedance boundary condition formulation which depend mainly on the choice of a field state variable and the solution technique applied.

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.

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.

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 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.

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.

This paper seeks to develop a sub‐domain perturbation technique to efficiently calculate strong skin and proximity effects in conductors within frequency and time domain finite element (FE) analyses.

A reference eddy current FE problem is first solved by considering perfect conductors. This is done via appropriate boundary conditions (BCs) on the conductors. Next the solution of the reference problem gives the source for eddy current FE perturbation sub‐problems in each conductor then considered with a finite conductivity. Each of these problems requires an appropriate volume mesh of the associated conductor and its surrounding region.

The skin and proximity effects in both active and passive conductors can be accurately determined in a wide frequency range, allowing for precise losses calculations in inductors as well as in external conducting pieces.

The developed method allows one to accurately determine the current density distributions and ensuing losses in conductors of any shape, not only in the frequency domain but also in the time domain. Therefore, it extends the domain of validity and applicability of impedance‐type BC techniques. It also offers an original way to uncouple FE regions that allows the solution process to be lightened, as well as efficient parameterized analyses on the signal form and the conductor characteristics.

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.

The purpose of this paper is to revisit the recursive computation of closed-form expressions for the topological derivative of shape functionals in the context of time-harmonic acoustic waves scattering by sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions).

The elliptic boundary value problems in the singularly perturbed domains are equivalently reduced to couples of boundary integral equations with unknown densities given by boundary traces. In the case of circular or spherical holes, the spectral Fourier and Mie series expansions of the potential operators are used to derive the first-order term in the asymptotic expansion of the boundary traces for the solution to the two- and three-dimensional perturbed problems.

As the shape gradients of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.

The authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function in the iterated numerical solution of any shape optimization or imaging problem relying on time-harmonic acoustic waves propagation. When coupled with converging Gauss−Newton iterations for the search of optimal boundary parametrizations, it generates fully automatic algorithms.