Can the shape of a drum be heard, or more precisely, is it possible to reconstruct the geometry of a vibrating membrane based on the knowledge of all of its natural vibration frequency? How can cracks in a component be detected by measuring temperature and heat flows (or the displacement and the forces applied) simultaneously on the edge of the component? Can the mechanical properties of a thin film of adhesive be identified by measuring the displacement and the forces at the end of a beam stuck on a more rigid substrate? How can the parameters of a model be adjusted on the basis of testing to make the model more realistic? Can the source of river pollution be detected by taking measurements downstream?

All of these questions involve the consideration of reverse problems: reverse rather than direct problems, i.e. the type of problems we generally face (calculation of the solution field of a partial differential equation or a differential equation when given limits and physical parameters are applied to an initial geometry and conditions).

These problems have long been little considered due to their "awkward" nature (sometimes no unique solution can be found, no continuity in the solution despite almost certain data).

However, with the computing power available today, methods have been developed enabling these problems to be solved. These problems are now integrated in research, but also in applications in all fields (industry, health, meteorology, etc.).

The aim of the EA is to explain the nature of a reverse problem and the main difficulties in solving this type of problem, to demonstrate using examples (and counter-examples!), and to deal with a few of the major methods and ideas behind resolution techniques.

Programme:
- 4 lectures + exercises
- 5 + 1 project-based modules

Examples of project subjects (students work in pairs) from past years:
- Electrical imaging of the sub-soil
- Identification of seal behaviour (adhesive between two beams)
- Identification of cracks in thermoelasticity using surface measurements (digital project)
- Extension of surface data to the inside of solids
• Detection strategies for sources of pollution in rivers
(for the list of subjects in 2008 look at the "documents pedagogiques" web page)

Numerus clausus:14

Last Modification : Monday 26 September 2011