Search

This paper presents the analysis of a transverse flux induction furnace. The originality of the analysis presented in this paper is to use successively three different formulations in order to solve the magneto-thermal coupled problem. The Whitney elements (node based, edge based, facet based and volume based elements) are shown to be a convenient mean to perform naturally that coupling and to fullfil convergence conditions for the iterative solver. Index terms - Coupling, eddy currents, electromagnetic heating, finite element methods, induction heating, thermal devices.

A new approach for error estimation in finite element computations is presented. This method may be applied to a wide range of modeling (magnetostatics, magnetodynamics, scattering problems). The main idea is to reconstruct, from the finite element solution of a primal formulation, a field belonging to the space of the dual finite element formulation. The error is then computed through the non fulfillment of the constitutive relation by the couple: primal solution-dual solution. 2-D problems with analytical solutions are treated to prove the efficiency of the method. Then the error estimator is used to adapt the mesh for a 3-D magnetostatic problem. Index terms - Error analysis, finite element method, adaptative meshing, modeling, magnetostatics, magnetodynamics.

Mixed formulations of Maxwell's equations are presented and the nature of the matrices appearing in these formulations is discussed. The point is made to their indefinite character. A method for solving these unusual matrices is then developed and applied to a test problem.

Several characteristics of magnetostatic and magnetodynamic mixed formulations are presented and discussed. The use of nodal, edge, facet and volume mixed elements enables their natural and rigorous discretization. Their advantages compared with conventional formulations are pointed out.

The paper presents a method to control the quality of finite element solutions using the error in constitutive relation. An a posteriori error estimator is built up. Its construction is general and gives quantitative results about the accuracy of the solution. Both problems of control of quality and mesh optimisation are also discussed. Several examples are presented.