13.1 Introduction

If the finite element method, modeling of electromagnetic problems by the finite elements, and meshing techniques initially had almost independent evolutions, this is no longer the case. Indeed, little by little, the modeling of electromagnetic fields has become more accurate, more rigorous and has been extended to new problems. In order to reach this goal, the finite element method is adapted and generalized. In the same way, mesh algorithms, which constitute a link between the numerical method and the geometric and physical approach, follow this evolution incrementally, and are integrated into the new numerical and mathematical methods, as well as into new growing problems. Thus, it is increasingly difficult to tackle these three topics, numerical methods, physics of magnetism and meshing, in a disconnected manner, because they are more and more closely interrelated.

A general analysis of meshing problems within the finite element method to electromagnetic field calculation is proposed. This chapter has several objectives: to display modern meshing techniques and present the current problems dealt with in electromagnetism so as to characterize their influences and their requirements in terms of meshing techniques.

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13.2 General Definition

In order to implement the finite element method independently of the physics of the phenomena we want to study, it is necessary to define a finished study domain on which we will seek a spatio-temporal distribution of the state variable which satisfies:

• partial differential equations, namely Maxwell's equations...