Abstract : This thesis deals with three-dimensional modelling of electric fields and magnetic fields by finite element method.
The first chapter devoted to the study of scalar problems include, in addition to the scalar formulation, a comprehensive analysis of the application of this formulation to the direct determination of integral quantities. Fluxes, capacities and inductances are calculated using the concept of co-energy. Evaluation of forces and torques uses the principle of virtual work. Clear philosophy of this methodology has led us to devise a method of evaluating the influence of geometric parameters and physical integral quantities.
In the second chapter we study the variational formulation of magnetostatics problems in which the field derives from a potential vector. The boundary conditions are the subject of special attention. The problem of uniqueness of the solution is solved by introducing a variational formulation which uses the principle of penalty. This formulation is developed in both cartesian and cylindrical coordinates: these later are particularly well suited to the study of rotating machinery. Of course, the application of this formulation to calculate integral quantities is derived from the direct method described in the first chapter.
In the third chapter, we approach the study of the general organization of computing software. We propose a structure of software that allows both two-dimensional and three-dimensional approach of optimization (automatic or assisted) in the best conditions.