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 to 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

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 aircraft and car industries, acoustics, solar cells, fans, etc.

Professor Olivier Pironneau’s research interests include Fluid Mechanics, Electromagnetism, Optimal Design, Mathematical Finance, Numerical Analysis and Partial Differential Equations. He is the author of 8 books and more than 300 papers and the Advisor of more than thirty Ph.D. students. He is a member of French Academy of Sciences and was awarded the Marcel Dassault Prize by the French Academy of Sciences in 2000. He is also the recipient of the Blaise Pascal Prize of the Academy of Sciences (1983), the Legion d’Honneur (2009), and is an Associate member of the Russian Academy of Sciences. His group has developed the software named FreeFEM which is used by researchers worldwide for computation.