Olivier Pironneau est professeur émérite au Laboratoire Jacques-Louis Lions de l'université Pierre et Marie Curie, Paris 6. Il est invité par la Fédération de Mathématiques de CentraleSupélec pour parler devant un public constitué à la fois de chercheurs et d'élèves.
Titre : Recherche des formes optimales avec les Mathématiques et l'Informatique.
Résumé :
There is an underlying assumption in sciences that once a system is understood it can be improved or controlled. However beyond a handful of parameters the human mind cannot find the optimum by trial, error and experience; one needs the help of computers and optimization algorithms.
Shape optimization may be hard to define mathematically because of conflicting criteria uncertainty in the data and topological problems, yet number of solutions are available.
Optimal design has invaded almost all fields of engineering; it can be as different as the design of the door of a car, which makes the most pleasing noise when slammed to the identification of oil reservoir underground.
Calculus of variations and optimization theory provide mathematical tools leading to computational algorithms to optimize shapes. But there are still a number of unsolved issues related global versus local optimization, multiple scales, and convergence of numerical methods.
Computer science provides also an entirely different set of tools derived from machine learning, cellular automata and computational graphics.
Many examples and solutions will be presented from airplane and car industries, acoustics, solar cells, fans, etc.