G. Meunier

Finite element modeling of unbounded problems using transformations: a rigorous, powerful and easy solution

A finite element method for the computation of open boundary problems using transformations is presented. The principle of the method is presented. A novel transformation, called the parallelepipedic shell transformation, is developed. This transformation and the manner of implementation of these techniques in Flux3d software lead to an efficient tool for modeling an open boundary problem by means of the finite-element method. Validation, results, and application are presented. >

Finite-element method modeling of superconductors: from 2-D to 3-D

A three-dimensional (3-D) numerical modeling technique for solving problems involving superconducting materials is presented. The model is implemented in finite-element method software and is based on a recently developed 3-D formulation for general electromagnetic problems with solid conductors. It has been adapted for modeling of superconductors with nonlinear resistivity in 3-D, characterized by a power-law E-J relation. It has first been compared with an existing and verified two-dimensional (2-D) model: Compared are the current density distribution inside the conductors and the self-field ac losses for different applied transport currents. Second, the model has been tested for computing the current distribution with typical 3-D geometries, such as corner-shaped and twisted superconductors. Finally, it has been used with two superconducting filaments in the presence of external magnetic field for verifying the existence of coupling currents. This effect deals with the finite length of the conductors and cannot be taken into account by 2-D models.

Simulation of induction machine operation using a step by step finite element method coupled with circuits and mechanical equations

The authors present the modeling of an induction machine using a nonlinear magnetodynamic complex method coupled with the circuit equations. The method is an extension to the harmonic solution of nonlinear magnetodynamic problems of the proposed classical finite element method. The coupling of the circuit equation completes the 2-D finite element method by making it possible to take into account the 3-D part of the motor. Another advantage is the ability to include voltage sources. >

Simulation of induction machine operation using complex magnetodynamic finite elements

The nonlinear magnetodynamic model implemented in FLUX2D is improved in order to solve the field equations in an induction motor with a highly saturated slot isthmus. The resulting method is an extension to the harmonic solution of nonlinear magnetodynamic problems using the classical finite-element method. This extension applies the nonlinear Newton-Raphson algorithm in the same way as for magnetostatic problems, using the Jacobian matrix presented. The forces and torques obtained by this algorithm are quite identical to those results obtained by a step-by-step simulation. Applied to an industrial four-pole, squirrel cage induction machine, this method gives over the whole range of speed an error less than 5%. >

Finite element modeling of open boundary problems

The authors explain how to compute open boundary problems in electromagnetism with good accuracy in the cases of two- and three-dimensional problems with existing classical finite-element method software. The proposed method is based on the use of an implicit spatial transformation to map the infinite exterior onto a finite domain; it requires very few modifications of code and is easy to implement in finite-element software. Comparisons with other methods show that the results are very good and that computer times are very competitive in relation to those of classical methods. Examples are given for 2-D Cartesian, 2-D axisymmetric, and 3-D problems. An advantage of the proposed method is that the matrix of the system to be solved is sparse and keeps a band structure, as in a classical finite-element problem. >

An original solution for unbounded electromagnetic 2D- and 3D-problems throughout the finite element method

A finite-element modeling of open boundary problems is presented and applied to magnetostatic problems in two and three dimensions. It is shown that computation of the magnetic field is achieved with a very good accuracy and good speed. It is noted that the general matrix formulation described permits the efficient use of a transformation more complex than that given by J. Imhoff et al. (1989). Implementation in existing finite-element software is very simple. Although the case of magnetostatic problems has been considered for simplicity, it is quite possible to apply the method to other kinds of problems (magnetodynamic ones or those for which a variational formulation is nonexistent). Such a technique of resolution of unbounded problems is really performant in comparison with other methods, and one of its advantages is the rapidity of calculation. >

A nonlinear circuit coupled t-t/sub 0/-/spl phi/ formulation for solid conductors

A new three-dimensional (3-D) finite element formulation based on the use of the magnetic scalar potential is proposed. It allows the description of multiply connected solid conductors coupled to electric circuits and to take into account the nonlinearities. Like the solutions using the magnetic vector potential, it is a general formulation and offers powerful solutions but at a lower cost.

Innovating approaches to the generation of intense magnetic fields : design and optimization of a 4 Tesla permanent magnet flux source

An original permanent magnet flux source is designed in order to generate a magnetic field of several Tesla. The magnet configuration and discretization of the structure are optimized with the help of numerical simulation software developed at LEG (DIPOLE-3D, FLUX2D & FLUX3D). The model of spheroidal flux source presented in the paper creates a field in excess of 4.3 T in a central volume of O 6 mm/spl times/h 2.8 mm with external diameter /spl ap/O100 mm. A prototype is in the final assembly stage, designed for X-ray dichroism experiments at the European Synchrotron Radiation Facility (ESRF) in Grenoble.

An approach for automatic adaptive mesh refinement in finite element computation of magnetic fields

An approach to the estimation of errors in adaptive finite-element mesh generation is discussed. The method is based on the analysis of the continuity of H and B at the boundaries between elements. Analyses are presented in two dimensions but can be utilized in three dimensions. The method is easy to use and can reduce the number of iterations of the mesh refinement process. >

Simulation of induction machines using complex magnetodynamic finite element method coupled with the circuit equations

The modeling of an induction machine using a nonlinear magnetodynamic complex method coupled with the circuit equations is presented. The squirrel cage rotor is a polyphase circuit with connection between bars and end-rings. Eddy currents induced in the bars are important, and the end-ring resistances have a considerable influence on the reaction of the rotor. Normally, the effect of the end-ring is taken into account by calculating an equivalent conductivity on the bar, but in using this method an error is made on the distribution of induced current density in the bar of the rotor and the effect of the end-ring inductance is forgotten. An induction squirrel cage machine can be modeled using a formulation which combines the analysis of magnetic fields with electrical circuit equations taking the squirrel cage as a polyphase cycling circuit. >