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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.

This paper discusses the perfectly matched layer method recently proposed for the computation of static or quasistatic fields in open boundaries. In particular it is shown how the method can be derived by means of a particular co‐ordinate transformation applied to a finite‐size isotropic domain surrounding the system of interest. The method is therefore equivalent to a trivial truncation from the point of view of both accuracy and computing time.

This paper aims to propose a hybrid method, called finite element method‐Dirichlet boundary condition iteration (FEM‐DBCI), for the computation of time‐harmonic eddy current problems inside a conductor heated by coils in 3D open‐boundary geometry.

The method assumes the electrical field as unknown on a mesh of tetrahedral edge elements. The heating power density inside the conductor is then computed and a steady‐state thermal analysis is performed on the same mesh of nodal tetrahedra to calculate the temperature distribution inside the heated piece, taking radiation and convection into account. A numerical example is also provided.

The method couples a differential equation for the interior problem in terms of the electric fields with an integral equation for the exterior one. The global algebraic system is efficiently solved in an iterative way.

The paper illustrates the computation of time‐harmonic eddy current problems inside a conductor heated by coils.

This paper aims to discuss various numerical implementations of the integral equation in the hybrid finite element method‐Dirichlet boundary condition iteration (FEM‐DBCI) method for the numerical solution of unbounded static and quasi‐static electromagnetic field problems.

Three numerical implementations are described and compared from the point of view of accuracy and complexity, by means of two examples regarding simple electrostatic problems.

The implementation by means of a pair of integration surfaces made of element sides leads to accuracy levels which are much better than that of a single surface (made of element sides) and only a little worse than that of a single surface connecting point in the middle of finite element sides.

The former implementations, however, are simpler since they are practically the same as that of a standard boundary element method integral equation.

The paper constitutes a useful guide to the implementation of the FEM‐DBCI method.

Charge iteration is an iterative procedure for the finite element computation of unbounded electrical fields, created by voltaged conductors. It makes use of a fictitious boundary, enclosing all the conductors, on which the electrical potential is first guessed and then iteratively improved according to the charge lying on the conductor surfaces. Highlights the theoretical foundations of the procedure outside any numerical context. From this useful insight, obtains a model which can aid the user in utilization of the numerical version of the procedure.

The Robin iteration procedure is a technique for the FEM computation of electromagnetic scattering fields in unbounded domains. It is based on the iterative improvement of the known term of a non‐homogeneous Robin condition on a fictitious boundary enclosing the scatterer. In this paper it is shown that the procedure is equivalent to the application of the Richardson method to a reduced system and that the use of GMRES significantly reduces the computational effort.

In this paper, the optimization of the shape of the magnetic channel inside a superconducting cyclotron is performed. The objective is to ensure a proper shaping and reduction of the intensity of the cyclotron magnetic field so as to facilitate the extraction of the charged particles. The optimization problem is solved by following two different approaches: a genetic algorithm and a simulated annealing approach. The relative advantages of each of the methods employed for the optimization of the magnetic channel are discussed.

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.

The purpose of this paper is to improve the accuracy of the integral equation of the hybrid FEM‐RBCI (Finite Element Method‐Robin Boundary Condition Iteration) method for the numerical solution of two‐dimensional electromagnetic (or acoustic) scattering problems.

This accuracy improvement is achieved by selecting the integration curve as straight segments lying in the middle of the triangular finite elements. An accuracy improvement is obtained as compared with selecting the integration curve as constituted by element sides.

The improved FEM‐RBCI method described in this paper leads to accuracies of the numerical results which are better than those obtained by selecting the integration curve by element sides.

The paper presents results for a simple two‐dimensional structure: a dielectric circular cylinder.

The optimization of the cross section of an axisymmetric induction heating device is performed by means of genetic algorithms (GAs).

The hybrid finite element method–Dirichlet boundary condition iteration method is used to deal with the unbounded nature of the field. The formulation of the electromagnetic problems takes into account skin and proximity effects in the source currents.

The convergence of GAs towards the optimum is very fast, since less than a thousand analyses have been necessary.

A special derivation of the finite element global system is presented which allows us to save computing time.