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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.

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.

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.

The purpose of this paper is to present a modified version of the hybrid Finite Element Method-Dirichlet Boundary Condition Iteration method for the solution of open-boundary skin effect problems.

The modification consists of overlapping the truncation and the integration boundaries of the standard method, so that the integral equation becomes singular as in the well-known Finite Element Method-Boundary Element Method (FEM-BEM) method. The new method is called FEM-SDBCI. Assuming an unknown Dirichlet condition on the truncation boundary, the global algebraic system is constituted by the sparse FEM equations and by the dense integral equations, in which singularities arise. Analytical formulas are provided to compute these singular integrals. The global system is solved by means of a Generalized Minimal Residual iterative procedure.

The proposed method leads to slightly less accurate numerical results than FEM-BEM, but the latter requires much more computing time.

Then FEM-SDBCI appears more appropriate than FEM-BEM for applications which require a shorter computing time, for example in the stochastic optimization of electromagnetic devices.

Note that FEM-SDBCI assumes a Dirichlet condition on the truncation boundary, whereas FEM-BEM assumes a Neumann one.

This paper aims to extend an efficient method to solve the global system of linear algebraic equations in the hybrid finite element method – boundary element method (FEM‐BEM) solution of open‐boundary skin effect problems. The extension covers the cases in which the skin effect problem is set in a truncated domain in which no homogeneous Dirichlet conditions are imposed.

The extended method is based on use of the generalized minimal residual (GMRES) solver, which is applied virtually to the reduced system of equations in which the unknowns are the nodal values of the normal derivative of the magnetic vector potential on the fictitious truncation boundary. In each step of the GMRES algorithm the FEM equations are solved by means of the standard complex conjugate gradient solver, whereas the BEM equations are not solved but used to perform fast matrix‐by‐vector multiplications. The BEM equations are written in a non‐conventional way, by making the nodes for the potential non‐coinciding with the nodes for its normal derivative.

The paper shows that the method proposed is very competitive with respect to other methods to solve open‐boundary skin effect problems.

The paper illustrates a new method to solve efficiently skin effect problems in open boundary domains by means of the hybrid FEM‐BEM method.

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.