A. Nicolet

Transformation methods in computational electromagnetism

The representation of electromagnetic quantities by differential forms allows the use of nonorthogonal coordinate systems. A judicious choice of coordinate system facilitates the finite element modeling of infinite or very thin domains.

Numerical computation of the magnetostriction effect in ferromagnetic materials

This paper describes a model of the magnetostriction by a finite element scheme for magnetostatic cases. Given a structure, the magnetic field is first computed taking into account the ferromagnetic saturation. Magnetic induction over elements is then used to compute the magnetoelastic energy and the minimization of the mechanical functional leads to the determination of displacement, strain, etc., due to the magnetostriction process.

Skin effect and proximity effect in multiconductor systems with applied currents and voltages

A finite element‐boundary element coupling method is used to compute the two‐dimensional magnetic field in multiconductor systems with magnetic materials. The terminal voltages and the tangential magnetic field on the boundaries are included in the finite element formulation for conductors. The total current in a conductor is expressed as the line integral of the tangential field around the conductor. One extra condition per conductor is necessary. It can be used to force the total current or, more generally, to couple the magnetic field computation program with circuit equations. Comparison between numerical results and analytical computations (a circular conductor and two rectangular bars in a slot) shows the accuracy of the method.

Analysis of ferroresonance with a finite element method taking hysteresis into account

Abstract This paper describes the analysis of ferroresonance in power systems with the help of 2D finite element method. It leads to the realistic evaluation of the nonlinear inductance behaviour. The effect of hysteresis on waveforms and the energy balances are analysed for various modes of ferroresonance.

Corner Modelling for BEM in Magnetostatic

The boundary element method provides very convenient models for two-dimensional magnetostatic problems. The basic equation is a Poisson equation involving the Laplace operator. Difficulties arise at special points such as corners. A method for solving the problem of geometrical singularities at the meeting point of n domains is presented. Some degenerated cases of practical interest are studied.

An Optimal Adaptative Numerical Integration Method

This paper presents an adaptative extension of the Gaussian integration method. It is well known that the Gaussian integration method is optimal for sufficiently smooth functions (i.e. which may be approximated by a polynomial) in the sense that it gives the maximum accuracy for a given number of nodes. Unfortunately it is not always possible to choose a priori the number of nodes for the integration. One alternative is to try successive Gaussian formulae with an increasing number of points until they agree with the required accuracy. In this case, most of the advantages of the method are lost. A less accurate but naturally adaptative method such as the Romberg method may become a better solution.

Comparison of various methods for the modeling of thin magnetic plates

Computation of the magnetic field in thin plates is particularly difficult because nodes on opposite sides of the plate are very close together and because the elements inside the plate are very flat. Three different methods, together with corresponding variations and combinations were used to compute the magnetic field in the plate: the boundary element method, the finite element method, and use of thin plate transmission conditions. With classical methods, the results are good for all cases, provided the computation of coefficients is sufficiently accurate. For very thin plates, a fine meshing is required to avoid failure of the computation. A new method that avoids those problems was designed. Since the vector potential varies very steeply across the plate, the idea is to replace the real plate by an equivalent double layer of current. The result is a special transmission condition, relating the values of the vector potential and of the tangential magnetic field on both sides of the plate. This conditi...

DDLMU, a software tool for the management of degrees of freedom in numerical modelization

A software tool is presented which is aimed to facilitate the development of large numerical programs such as the ones using the finite element method and the boundary element method (see Nicolet [1]). DDLMU is a module written in FORTRAN 77 and is aimed at performing tasks such as the degrees of freedom and equations numbering and the system assembling and resolution.

Comparison of Pure and Coupled BEM Methods for the Study of a Thin Plate Induction Oven

This paper presents the use of a magnetic field computation software (LUCBE-2D) to determine eddy currents in a thin plate induction oven. The major difficulty arises from the characteristics of the plates which are magnetic, conducting, long (500 mm) and thin (1mm). Various models are compared: one boundary element model of the plate and two finite element models of the plate differing from the meshing. In the three cases, the air around the plate is modelled by the boundary element method. It appears that the skin depth, naturally involved in the BEM formulation, must be taken into account explicitly for the meshing in the FEM formulation.

DDLMU, Degrees of Freedom Management Module for Numerical Modelization

A software tool is presented which is aimed to facilitate the development of large numerical programs such as the ones using the finite element method (seeb Silvester [1]) and the boundary element method (see Brebbia [2]). DDLMU is a module written in FORTRAN 77 and is aimed at performing tasks such as the degrees of freedom and equations numbering and the system assembling and resolution.