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

Perfectly matched layers (PMLs) are used to truncate the mesh in a 3D edge finite element code. A new interpretation of the PMLs helps to solve the problem of joining PMLs of different directions and to estimate the proper setting of the PML parameters. The finite element code uses an A,V description to obtain a better convergence rate of the iterative solver. The program is used to model the electromagnetic field of a linear dipole antenna in the vicinity of lossy objects.

Parameter estimation for PMLs used with 3D finite element codes

This paper presents an improved physical phase variable model for electric drive simulations of permanent magnet machines. Emphasis is put on the accuracy of the mechanical behavior of the machine model and this makes the improved model suitable for noise and vibration investigations. Furthermore, the data storage scheme and interpolation method for the look up tables are revised and a memory and time efficient approach is suggested. This makes the new model also applicable for use in real time applications (e.g. drive controllers). Several comparisons of transient simulations between a finite element model and the model presented in this work illustrate the advantages of this method.

An improved physical phase variable model for permanent magnet machines

Linear antenna arrays consisting of dipole antennas find wide applications in wireless communication systems. Typically, arrangements with uniform spacing between the array elements are applied to gain highly directive radiation patterns. In the present paper an antenna array arrangement with non-uniformly spacing between the array elements is synthesized in the multi-objective sense. The optimization relies on the firefly algorithm and the PEEC method.

PEEC-based multi-objective synthesis of non-uniformly spaced linear antenna arrays

Purpose – The purpose of this paper is to analyse the eigenforms and eigenfrequencies of stator core stack by experimental and numerical investigation. The influence of material parameters on the structural vibrations is carried out in order to describe the laminated structure of stator core stack with a homogeneous material model. Design/methodology/approach – The finite element method is applied for a numerical modal analysis. Therefore, a homogeneous transversally isotropic material model is introduced and the influence of each material parameter on the dynamical behavior is investigated. These material parameters are stepwise adjusted to the results from the experimental modal analysis. The investigation includes results from different stator core stacks. Findings – The influence of material on the modal parameters is shown. Furthermore, material parameters are carried out for stator core stacks, which describe the measured dynamical behaviour. Originality/value – The presented investigations show a u...

Numerical and experimental investigation of the structural characteristics of stator core stacks

Summary. The nodal finite element realization of the T - n method involving a gauged current vector potential, T, is shown to yield erroneous results if applied to 3D eddy current problems with reentrant corners in the conducting region. The reason for the problem is pinpointed to be the implicit gauging of the vector po­ tential. A remedy of using no gauge in elements around the reentrant corners is suggested.

Oszkar Biro

Papers

Parameter estimation for PMLs used with 3D finite element codes

An improved physical phase variable model for permanent magnet machines

PEEC-based multi-objective synthesis of non-uniformly spaced linear antenna arrays

Numerical and experimental investigation of the structural characteristics of stator core stacks

Gauged Current Vector Potential and Reentrant Corners in the FEM Analysis of 3D