Calculs éléments finis paramétrés à l'aide des dérivées d'ordre élevé, Applications à l'électromagnétisme
In this work, a procédure of high order sensitivity analysis was implemented within the fînite élément method (FEM). Firstly, we presented the fundamental of this approach: the classical FEM and the essential high order derivative method which émulâtes the results in form of the Taylor's developments that report to the sensitivity parameters. Next, basing on a typical FE analysis, we hâve developed the modules of a parametrized analysis: the géométrie parametrization, the mesh dérivation and the parametrized solving stage. The originality of this implementation consists firstly of using the symbolic opérations in a new organisation of the derivatives caîculus. A number of the examples was done for validating ail the created tools. In the end, the possible applications of the parametrized results were evoked; among those, we propose the procédure that will allow us to define the équivalent analytical model of electromagnetic device. The numerous problems related to the software achievement are taken on évidence and solved, which represent the heavy investment in programming. Several clear perspectives are opened, however, by this approach and the pursuits of the developments will achieve their merit.