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The scope of the work is to provide an identification procedure for an hysteresis model based on nonlinear circuit cells.

An identification procedure for an hysteresis model based on nonlinear circuit cells is presented. The response of elementary cell is equal to a generalized play operator. The procedure allows the identification of the limit symmetric hysteresis loop and of minor loops. The identification procedure is based on the relationship between the circuit parameters and the discretization of the first derivative of the BH curve by means of a staircase function.

The model obtained is employed for the simulation of soft magnetic composite material cores under different supply voltage waveforms. The proposed identification procedure is able to define an accurate model of an hysteretic material with a low number of elemental network cells. The identification algorithm is simple and makes use of the limit hysteresis cycle only. Symmetric minor loops are used to tune “soft” operators for the correct reconstruction of cycles which do not reach saturation.

The model is limited to scalar and static hysteresis model.

The model obtained can be used in network simulator like SPICE in order to model circuits in which magnetic devices are involved.

The circuit hysteresis model has been presented in literature, while its identification is newly proposed by the authors.

This work aims to present a multilevel optimization strategy based on manifold‐mapping combined with multiquadric interpolation for the coarse model construction.

In the proposed approach the coarse model is obtained by interpolating the fine model using multiquadrics in a small number of points. As the algorithm iterates the response surface model is improved by enriching the set of interpolation points.

This approach allows to accurately solve the TEAM Workshop Problem 25 using as little as 33 finite element simulations. Furthermore, it allows a robust sizing optimization of a cylindrical voice‐coil actuator with seven design variables.

Further analysis is required to gain a better understanding of the role that the initial coarse model accuracy plays in the convergence of the algorithm. The proposed model allows to carry out such analysis by varying the number of points included in the initial response surface model. The effect of the trust‐region stabilization in the presence of manifolds of equivalent solutions is also a topic of further investigations.

Unlike the closely related space‐mapping algorithm, the manifold‐mapping algorithm is guaranteed to converge to a fine model optimal solution. By combining it with multiquadric response surface models, its applicability is extended to problems for which other kinds of coarse model such as lumped parameter approximations for instance are tedious or impossible to construct.

The scope of the work is to provide an hybrid numerical technique for the solution of electric field.

In this paper an integral approach for the solution of static electric field based on a dual discretization (DD) and on a surface method of moment (MoM) is presented. The proposed technique is applied to the solution of 3D electric field problems where different perfectly conducting bodies are placed in a homogeneous and isotropic medium. The approach is also extended to the analysis of static current field. In the presented formulation MoM is applied on a surface domain which is discretized according to a baricentrical dual scheme.

The procedure has been applied to several practical cases and it represents an efficient tool for the evaluation of lumped circuit parameters as capacitances of 3D conducting bodies and ground resistance of grounding systems.

The formulation presented in the paper is limited to the calculus of electric field in homogeneous media. For future development the authors are working in order to include non‐homogeneous media.

The proposed approach aids the designer of electrical systems as large scale grounding systems or integrated circuit connections in the calculations of lumped electrical parameters.

The originality of the paper lies in the coupling of MoM with finite formulation and DD.

To apply two different integral formulations of full‐Maxwell's equations to the numerical study of interconnects in a low‐frequency range and compare the results.

The first approach consists of a surface formulation of the full‐Maxwell's equations in terms of potentials, giving rise to a surface electric field integral equation. The equation, given in a weak form, is solved by using a finite element technique. The solenoidal and non‐solenoidal components of the electric current density are separated using the null‐pinv decomposition to avoid the low‐frequency breakdown. The second model is an extension of partial element equivalent circuit technique to unstructured meshes allowing the use of triangular meshes. Two systems of meshes tied by duality relations are defined on multiconductor systems. The key point in the definition of the equivalent network is to associate the pair primal edge/dual face to a circuit branch. Solution of the resulting electrical network is performed by a modified nodal analysis method and regularization of the outcoming matrix is accomplished by standard techniques based on the addition of suitable resistors.

Both the formulation have a regular behaviour at very low frequency. This is automatically achieved in the first approach by using the null‐pinv decomposition.

Surface sources of fields.

Two different integral formulations of full‐Maxwell's equations for the numerical study of interconnects are compared in terms of low‐frequency behaviour.

The purpose of this paper is to obtain a fully analytical model of an eddy current coupler and to use it in a multi‐objective optimisation algorithm.

Analytical expressions of device performances are adopted in the objective function and are obtained from a closed solution of the field problem. The optimisation has been carried out by considering both the torque and the momentum of inertia of the object. Two different structures have been considered.

A fully analytical expression of the torque has been obtained for two different geometrical configurations. The optimisation procedure has been used to compare these structures and it is possible to observe that the DSPM performances are better than the SSPM ones.

To obtain a closed form of the torque function, the non‐linearities of the iron have been neglected. Nevertheless, in the optimisation procedure has been limited the magnetic flux density in the iron core to a feasible value in the linear part of the ferromagnetic characteristic. The thermal effects have been neglected.

In the industry, eddy current couplers can be used as transmission, dampers and brakes. The use of objective functions (OFs) in a closed formulation allows to perform a light optimisation from the point of view of the time computation and to drastically increase the development efficiency.

In this paper, a model for computing the electromagnetic behaviour of eddy current couplers is presented. The optimisation of both the torque and the inertia momentum allows to obtain good static and dynamic performances.

The optimisation of a tubular linear motor with interior permanent magnets is described. For a rapid design the whole process is divided in three parts: an analytical approach for the a preliminary investigation, a parametric analysis by means of a finite element method and an optimisation. The obtained results show that the adopted optimisation process is efficient for rapid and effective optimisation of the tubular linear motor.

The paper aims to describe the coupling of magnetostatic finite formulation of electromagnetic field with two integral methods.

The first hybrid scheme is based on Green's function applied to magnetization source while the other one is based on a magnetic scalar potential boundary element method. A comparison of the two techniques is performed on a benchmark case with analytical solution, on a 2D multiply‐connected problem and on an industrial case where measurements are available.

The proposed hybrid approaches have proved to be effective techniques to solve open boundary non‐linear magnetostatic problems. Similar convergence speed with respect to the number of unknowns is found for both schemes

The paper shows the effectiveness of hybrid schemes applied to the finite formulation, assessing their performances on various test cases.

To propose a novel 3D hybrid approach, based on a discrete formulation of Maxwell equations (the cell method – CM), suitable for solving eddy current problems in unbounded domains.

Field equations for magnetodynamics are expressed directly in algebraic form thanks to the CM. The eddy current problem inside bulk conductors is formulated in terms of discrete modified vector potential, whereas magnetic scalar potential is used in order to model the free space. The CM is coupled to the boundary element method by using a surface boundary operator, which maps the surface magnetic fluxes to the surface magnetic scalar potentials. This leads to a unique set of linear equations to be solved in terms of discrete potentials. The eddy currents in bulk conductors are then obtained from discrete potentials.

It is shown that formulation of hybrid approaches can be simplified by expressing field equations directly in algebraic form without need of weighted residual techniques. An original strategy, based on Green's formula for the magnetic scalar potential, is proposed in order to couple conducting parts to the exterior domain.

Conducting bodies with multiply connected parts cannot be modelled by the proposed approach, since it is based on the magnetic scalar potential. The resulting global matrix is partially dense and non‐symmetric; therefore, standard iterative solvers such as GMRES have to be used.

The proposed approach can be suitably used for analyzing eddy current problems involving models with high degree of complexity, large air domains and moving parts. These are typical of induction heating processes.

This paper proposes a new 3D hybrid approach, based on a discrete formulation of Maxwell equations. A novel coupling strategy relying on integral electromagnetic variables, i.e. magnetic fluxes and magnetic scalar potentials, is devised in order to solve uniquely for eddy currents inside conducting bodies.

Shielding of electromagnetic low frequency field can be performed by means of conductive sheets. These sheets have a thickness which is usually two or three orders of magnitude lower than their other dimensions, thus their effects must be modeled by means of special numerical techniques. In this paper, two integral formulations for the analysis of conductive shields are presented: one is two‐dimensional and is based on a multiconductor system, while the other, three‐dimensional, is based on a finite formulation of electromagnetic fields. Once these analysis tools have been introduced, this paper presents the study of different shielding systems and a problem of optimal exploitation of conductive material.

Introduces the fourth and final chapter of the ISEF 1999 Proceedings by stating electric and magnetic fields are influenced, in a reciprocal way, by thermal and mechanical fields. Looks at the coupling of fields in a device or a system as a prescribed effect. Points out that there are 12 contributions included ‐ covering magnetic levitation or induction heating, superconducting devices and possible effects to the human body due to electric impressed fields.