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Linear hexahedral and tetrahedral elements are joined without linking elements of pyramidal shape. Two triangular faces are constrained by a quadrilateral face in irregular meshes with hanging edges. Edge shape functions are not conforming on the interfaces. Test computations showed good accuracies in the results by the method comparing with results using meshes made of linear hexahedral, tetrahedral and quadratic-nodal-linear-edge elements. The hybrid mesh makes mesh generations flexible and overcomes the degradation of results using the linear tetrahedral edge elements with high aspect ratio for conductive regions in eddy current analyses. The quadratic-nodal-linear-edge elements were also studied and remedy the degradation of linear tetrahedral elements. Index Terms--Eddy current analysis, edge elements, finite-element method (FEM), hybrid mesh.

The conventional finite-element method (FEM) deteriorates the convergence characteristic of the incomplete Cholesky conjugate gradient (ICCG) method in magnetic field analyses when there are extreme thin elements in meshes. The convergence characteristic is drastically improved by a proposed method, where common unknown variables are simply added to near parallel edges. The number of unknowns is increased, but the rank of the equation is not changed and the condition of the matrix becomes better. The method for thin elements presented in the paper is an application of 'singularity decomposition technique' (SDT) in common with the A-[phi] formulation and the implicit correction multigrid method. Index Terms--Finite-element method (FEM), incomplete Cholesky conjugate gradient (ICCG) method, magnetic field analysis, singularity decomposition technique (SDT), thin element.

This paper presents a novel method for analyzing transient magnetic fields in laminated iron cores. It is based on the finite-element method and a newly developed homogenization method is applied to model the lamination effectively. The homogenized constitutive relations, of which the approximation is only applicable to low-frequency problems, are derived analytically, neglecting eddy currents induced by time-varying magnetic fluxes parallel to the lamination. The loss due to the neglected eddy currents is estimated in the postprocessing state utilizing the obtained magnetic field variation. The calculated magnetic field is in good agreement with the measurement for a benchmark problem. It is demonstrated that the homogenized relations can be applied to the low-frequency problems. Index Terms--Anisotropic nonlinear magnetic field analysis, homogenization method, iron loss, laminated iron core.

In order to calculate the eddy current losses in the thin surface layer of a laminated core, in which the insulation between steel sheets is broken by a process of a polish, the leaf element is expanded into the edge finite element method. Several treatments for the leaf element are illustrated and the effectiveness is investigated by using a simple model. Then, the effect of the surface layer on the iron losses is discussed in an actual magnetic bearing system. Index Terms--Finite element method, laminated core, leaf element, magnetic bearing.

A line search was combined with the Newton-Raphson method to accelerate the convergence of the iterative calculation in nonlinear magnetic field analysis. As a method for determining a step size for update, the minimization of an energy functional and a square of 2-norm of residual obtained from the finite-element discretization was investigated. It was demonstrated that the energy functional minimization is superior to the residual minimization from the viewpoint of computational cost. The line search is effective even in the magnetic vector potential formulation, which is said to be stable usually. Index Terms--Energy functional, line search, minimization, Newton--Raphson method, nonlinear magnetic field analysis, residual.

In order to examine the accuracy of the Nodal Force Method, a comparative study of the FEM solution has been performed which includes the edge element and the nodal element formulations. The treatment when the Maxwell stress tensor becomes asymmetric has also been investigated. Index terms - Magnetic forces, finite element methods, Maxwell stress tensor, nodal force method, edge element.

A new type of second order edge elements for simplexes (triangles and tetrahedra) is proposed. The element is geometrically symmetric and the shape functions are orthogonal to each other in the integrals of the tangential components on edges. The number of nodes and edges are 14 and 24 in a tetrahedral element. The proposed elements are validated by eigenmode calculations in a cavity using newly developed method to solve eigenvalue problems with large matrices. Highly accurate eigenvalues are calculated using the elements. Index terms - Edge elements, eigenvalue problems

A newly developed integral method for the static magnetic field analyses in shell structures is presented. The system matrix in weak form is symmetric and the magnetization i s represented by triangular vector finite elements preserving continuity of the normal components across element boundaries. The validity of this method is confirmed by calculating test shielding problems. The results by this method agree with the results by the finite element method and the analytical solution.

This paper describes eddy current analyses using the integral method and dynami deflection analyses using the finite element method taking coupling effects int consideration. The electromotive force due to the deflection is obtained by moving the coordinates of the discretized nodes according to the results of the deflection analyses in the Lagrangian coordinate system. The calculated results are in good agreement with the experimental results of TEAM Workshop Problems 1 and 16. The importance of the coupling effect in a fusion device is shown by th calculated results of a cylinder for plasma disruption with downward motion.

SUMMARY Electromagnetic phenomena intrinsically spread over an infinite region. Thus, efficient handling of open boundaries is one of the main issues in electromagnetic field computations. This paper deals with the orthogonalized infinite edge element method that efficiently performs precise analysis of the infinite region. In this method, several parameters are used to achieve high accuracy. As one of the parameters, we focus on the reference point and investigate the effect of its position setting on accuracy. We also evaluate the accuracy of the calculated magnetic field in the far region. By applying boundary element method as postprocessing, it is found that high computational accuracy in the region can be effectively achieved. [ABSTRACT FROM AUTHOR]

This paper describes a benchmark model proposed for the clarification of the characteristic of various methods for modeling the laminated iron core. In order to obtain a reference solution of the benchmark model, a large-scale nonlinear magnetostatic field analysis with a mesh fine enough to represent the microscopic structure of the laminated iron core is carried out by using the hybrid finite element–boundary element (FE-BE) method combined with the fast multipole method (FMM) based on diagonal forms for translation operators. The computational costs and accuracy of two kinds of homogenization methods are discussed, comparing them with the reference solution. As a consequence, it is verified that the homogenization methods can analyze magnetic fields in laminated iron core within acceptable computational costs. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 170(1): 26–35, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20809 [ABSTRACT FROM AUTHOR]