There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Introduction to Electromagnetic Compatibility

The finite-element method (FEM) is a full-wave numerical method that discretizes the variational of a functional. The evolution of this method within the scope of electromagnetics traces back to the solving of two classes of problems, namely, the eigenmode problems and the deterministic problems. If we try to use some examples to illustrate the most typical and the most complete techniques with the most complete solution, the eigenmode problem of a dielectrically loaded waveguide and the wave propagation in a three-dimensional (3D) discontinuous waveguide are good candidates representing the eigenmode and the closed-domain solutions, respectively. As for the open-domain scattering problem and radiating problems, the authors consider the essential and key parts are presented in solving the 3D scattering problems. For this reason, we will illustrate the theoretical basics, the critical solving techniques and the typical skills involved in FEM through solving of the above three specific problems. At the end of this chapter, we will also briefly review the FEM solution for some other problems.

Finite-Element Method

Various magnetic vector potential formulations for the eddy-current problem are reviewed. The uniqueness of the vector potential is given special attention. The aim is to develop a numerically stable finite-element scheme that performs well at low and high frequencies, does not require an unduly high number of degrees of freedom, and is capable of treating multiple connected conductors. >

On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents

Numerical Methods for Scientists and Engineers

Purpose – For an accurate simulation of the temperature distribution inside an electrical machine a method for deriving the convective heat transfer coefficient numerically would be desirable. The purpose of this paper is to present a reliable simulation setup, which is able to reproduce the measured convective heat transfer coefficient at certain spots on the end windings of an electric machine.Design/methodology/approach – The heat flux density on certain spots on the end windings of an induction motor have been measured with heat flux sensors, in order to find out the convective heat transfer coefficient. To identify the air mass flow inside a cooling duct of an encapsulated cooling circuit during the operation of the motor, the pressure loss inside the duct has been measured. The measured data for temperature and air mass flow have been used as boundary conditions for the identification of the convective heat transfer coefficient with a commercial software for computational fluid dynamics (CFD).Findin...

Measurements and Simulations of the Heat Transfer on End Windings of an Induction Machine

The relation between the output of the fluxset sensor and the magnetic field is established by the numerical and experimental investigation of an ECT set‐up. A fast calculation method has been developed for obtaining the magnetic field generated by the interaction of the probe and the crack in a finite plate by superimposing the results obtained by the analysis of a finite plate without a crack and an infinite plate with a crack. The calculations are made by FEM and boundary integral methods, respectively. The relationship between the measured output and the magnetic field is obtained by calculating the calibration factors giving the best fit of the two sets of data. Based on the results, a numerical tool is developed for the quantitative evaluation of magnetic field sensors applied to the measurement of spatially inhomogeneous fields.

Calculation of the field map from the measurement data of the fluxset sensor

A numerical procedure based on the Bubnov-Galerkin method is presented for the 
approximate solution of a nonlinear stationary magnetic field problem with inhomogeneous 
boundary conditions. Neumann-type boundary conditions are included in the operator 
equation describing the boundary value problem. Their incorporation is presented both with the 
aid of a special functional Hilbert space and by the use of generalized functions. The Dirichlet-
type boundary conditions are reduced to ones of Neumann type.

Application of the bubnov-galerkin method to nonlinear stationary magnetic field problems with inhomogeneous boundary conditions

Solving electromagnetic wave propagation problems with the finite-element method results in a large number of unknowns due to the necessity of modeling an extensive portion of the surroundings of the conducting structures. These equation systems are often ill-conditioned because of the great material differences as well as changes in size between neighboring elements. In addition, the resulting matrices are indefinite. Common iterative methods exhibit poor convergence due to these conditions. Direct solution techniques result in high memory requirements. The aim of this article is to present an approach with smaller memory demand than the direct methods and better convergence properties than common iterative techniques. An iterative method based on domain decomposition is presented and compared to various conventional iterative and direct solution techniques.

An Iterative Domain Decomposition Method for Solving Wave Propagation Problems

Two formulations to take account of eddy currents involving the simulation of rotating conductors are examined. The method based on the Minkowski transformation is used as reference for a non-conforming mesh method based on interpolation techniques. As an example, the two formulations are applied to a problem involving a coil rotating inside a conducting cylinder.

Oszkar Biro

Papers

Measurements and Simulations of the Heat Transfer on End Windings of an Induction Machine

Calculation of the field map from the measurement data of the fluxset sensor

Application of the bubnov-galerkin method to nonlinear stationary magnetic field problems with inhomogeneous boundary conditions

An Iterative Domain Decomposition Method for Solving Wave Propagation Problems

Comparison of two formulations taking account of 3D motion induced eddy currents