Physical and geometric singularities modelling techniques for electrostatics and electromagnetism problems

Singularities appear in many problems in electrical engineering. They may be geometric (for example peaks, corners or ridges in Electrostatics) or physical (for example, changes in electromagnetic properties on thin depths). Classical numerical methods like finite elements technique are badly adapted to the simulation of these singularities. The authors present the techniques that they have developed to take these singularities into account. It consists of crack elements in eddy current non destructive testing, and of bilinear elements to control insulating materials. The particularity of these techniques is the association of a numerical resolution using finite elements technique, with an analytical resolution using singular elements. The authors recall, moreover, the techniques introduced in their Boundary Integral Equations package, in order to take into account geometrical singularities in electrostatic problems.