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Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.

The use of electrohydraulic systems is becoming more widespread in industry. The control valve forms a vital component of any such system as it performs both power conversion and amplification. The valve is operated by a solenoid mounted on the end of the valve block. A typical solenoid actuator is shown in Fig. 1. Current through the coil generates a magnetic potential difference across the air‐gap, producing an attractive force between the opposing pole face and armature. The armature moves to close the air‐gap and minimize the reluctance of the magnetic circuit.

The paper presents an extension to previous work on modelling AC losses in high‐temperature superconducting tapes as a highly non‐linear diffusion process. Following successful formulation for a bulk superconductor the presence of silver in a tape has now been included, using a “sandwich” model, to represent more realistically the practical arrangement. The results of the extended 1‐D model are included and a new 2‐D scheme is described using finite difference formulation. Effects of non‐linearity are emphasised.

The purpose of this paper is to develop and systemize the 3D finite element (FE) description of electromagnetic field in electrical machines.

3D FE models of electrical machines are considered. The model consists of FE equations for the magnetic field, equations describing eddy currents and equations, which describe the currents in the machine windings. The FE equations are further coupled by the electromagnetic torque to the differential equation of motion. In the presented field‐circuit model, the flux linkages with the windings are expressed by two components. Attention is paid to the description of machine winding. Both scalar and vector potential formulations are analysed. The FE equations are derived by using the notation of circuit theory. The methods of movement simulation and torque calculation in FE models are discussed.

Proposed circuit description of electromagnetic field in electrical machines conforms to the applied method of electric and magnetic circuit analysis. The advantage of the presented description is that the equations of field model can be easy associated with the other equations of the electric drive system.

The applied analogies between the FE formulation and the equivalent magnetic and electric network models help formulate efficient field models of electrical machines. The developed models after coupling to the models of supply and control system can be successfully used in the analysis and design electric drives.

Ceramic superconductors experience losses when carrying alternating currents. A first step in an attempt to macroscopically model the loss mechanism is to consider the ac transport current in a ribbon that has a cross‐section of width much greater than thickness. To some extent high‐temperature superconductors behave in a way similar to type II superconductors in which the loss mechanism is described by the critical state model, where the current is assumed to flow with a constant critical density Jc and is independent of the magnetic flux density B and ∂B/∂t. The dominant mechanism is the irreversible motion of fluxoids due to their interaction with the pinning sites, resulting in a form of hysteretic loss that can be represented in macroscopic terms (in a system with only one component of magnetic field) as proportional to ∫HsdBa/T over a complete cycle of period T, where Hs is the surface magnetic field strength and Ba is the space average value of flux density. However, it is found that the high‐temperature materials exhibit strong flux creep effects, and so the critical state model may not provide a sufficient description. To find an alternative formulation it is necessary to consider the flux creep E‐J characteristic of the ceramic material. If a highly nonlinear expression for the resistivity ? can be found, it may be possible to model the flux and current behaviour as a diffusion process.

Numerical three-dimensional formulations using vector potential A have been examined for magnetic fields, with emphasis on the finite difference (FDM) and edge element (EEM) methods, with the view to establish common features. The paper aims to discuss these issues.

It has been shown that for hexahedral elements the FDM equations may be presented in the form similar to the EEM equations, providing the products of the nodal potentials and distances between the nodes are used as unknowns in FDM, instead of the usual nodal potentials.

The analogy between the FDM and the EEM approach has been established.

It has been demonstrated, following from this and previous publications, that analogy exists between all fundamental methods of field solutions relying on space discretisation. This is helpful in terms of classification of the methods and aids the understanding of physical processes involved.

The purpose of this paper is to develop a reluctance‐resistance network (RRN) formulation for determining the induced current distributions in a 3D space of multiply connected conducting systems.

The proposed RRN method has been applied to solve Problem No. 7 of the International TEAM Workshops. The induced currents in the conductive plate with an asymmetrically situated “hole” have been analysed. The RRN equations have been formed by means of the finite element method using the magnetic vector potential A and the electric vector potentials T and T₀. The block relaxation method combined with the Cholesky decomposition procedure has been applied to solve the resultant RRN equations.

Comparison with results published in literature has demonstrated high accuracy of the proposed RRN computational scheme while offering significant savings in computing times.

A novel formulation of the RRN approach has been proposed and demonstrated to be computationally efficient.

The aim of this paper is to access performance of existing computational techniques to model strongly non‐linear field diffusion problems.

Multidimensional application of a finite volume front‐fixing method to various front‐type problems with moving boundaries and non‐linear material properties is discussed. Advantages and implementation problems of the technique are highlighted by comparing the front‐fixing method with computations using fixed grids. Particular attention is focused on conservation properties of the algorithm and accurate solutions close to the moving boundaries. The algorithm is tested using analytical solutions of diffusion problems with cylindrical symmetry with both spatial and temporal accuracy analysed.

Several advantages are identified in using a front‐fixing method for modelling of impulse phenomena in high‐temperature superconductors (HTS), namely high accuracy can be obtained with a small number of grid points, and standard numerical methods for convection problems with diffusion can be utilised. Approximately, first order of spatial accuracy is found for all methods (stationary or mobile grids) for 2D problems with impulse events. Nevertheless, errors resulting from a front‐fixing technique are much smaller in comparison with fixed grids. Fractional steps method is proved to be an effective algorithm for solving the equations obtained. A symmetrisation procedure has to be introduced to eliminate a directional bias for a standard asymmetric split in diffusion processes.

This paper for the first time compares in detail advantages and implementation complications of a front‐fixing method when applied to the front‐type field diffusion problems common to HTS. Particular attention is paid to accurate solutions in the region close to the moving front where rapid changes in material properties are responsible for large computational errors.

The purpose of this paper is to emphasise the analogies between variational and network formulations using geometrical forms, with the purpose of developing alternative but otherwise equivalent derivations of the finite element (FE) method.

FE equations for electromagnetic fields are examined, in particular nodal elements using scalar potential formulation and edge elements for vector potential formulation.

It is shown how the equations usually obtained via variational approach may be more conveniently derived using integral methods, employing a geometrical description of the interpolating functions of edge and facet elements. Moreover, the resultant equations describe the equivalent multi‐branch circuit models.

The approach proposed in the paper explores the analogy of the FE formulation to loop or nodal magnetic or electric networks and has been shown to be very beneficial in teaching, especially to students well familiar with circuit methods. The presented methods are also helpful when formulating classical network models. Finally, for the first time, the geometrical forms of edge and facet element functions have been demonstrated.

Design and optimisation of many practical electromechanical devices involve intensive field simulation studies and repetitive usage of time‐consuming software such as finite elements (FEs), finite differences of boundary elements. This is a costly, but unavoidable process and thus a lot of research is currently directed towards finding ways by which the number of necessary function calls could be reduced. New algorithms are being proposed based either on stochastic or deterministic techniques where a compromise is achieved between accuracy and speed of computation. Four different approaches appear to be particularly promising and are summarised in this review paper. The first uses a deterministic algorithm, known as minimal function calls approach, introduces online learning and dynamic weighting. The second technique introduced as ES/DE/MQ – as it combines evolution strategy, differential evolution and multiquadrics interpolation – offers all the advantages of a stochastic method, but with much reduced number of function calls. The third recent method uses neuro‐fuzzy modelling and leads to even further economy of computation, although with slightly reduced accuracy of computation. Finally, a combined FE/neural network approach offers a novel approach to optimisation if a conventional magnetic circuit model could also be used.