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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.

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 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.

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.

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.

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.

The operating activities section of the statement of cash flows presents a long-standing teaching challenge for accounting educators. The direct method is easy to understand yet difficult to prepare; the indirect method is harder to understand but easier to prepare. Many instructors address the two methods separately, requiring students to learn two different ways for preparing the operating section of a statement of cash flows. Because of this focus on the mechanics of preparation, the result is often an emphasis on how to prepare the cash flow statement rather than on the essential information the statement provides. In this paper, the authors note that both direct and indirect methods begin at the same point, that is, the income statement, and end at the same point, that is, cash flow from operations. Then, the authors describe one process by which the income statement and the balance sheet can be analyzed to provide the information required to present operating cash flow using either the direct or the indirect method. Using this approach allows students to apply one intuitive process for computing cash flow from operations rather than memorizing two different sets of rules for direct and indirect methods.

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.

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 purpose of this paper is to compare the hybrid FEM-BEM and FEM-DBCI methods for the solution of open-boundary static and quasi-static electromagnetic field problems.

After a brief review of the two methods (both coupling a differential equation for the interior problem with an integral equation for the exterior one), they are compared in terms of accuracy, memory and computing time requirements by means of a set of simple examples.

The comparison suggests that FEM-BEM is more accurate than FEM-DBCI but requires more computing time.

Then FEM-DBCI appears more appropriate for applications which require a shorter computing time, for example in the stochastic optimization of electromagnetic devices. Conversely, FEM-BEM is more appropriate in cases in which a high level of precision is required in a single computation.

Note that the FEM-BEM considered in this paper is a non standard one in which the nodes of the normal derivative on the truncation boundary are placed in positions different from those of the potential.