The objective is to investigate the influence of design spaces, generated by different representations of the changes of the shapes, on the cost of aerodynamic optimization. On one hand Radial Basis Function (RBF) representations, and on the other partial differential equations (ordinary differential equations for 2D shapes) must be investigated. The behaviour of those representations of the shape deformations in the context of optimization has hardly been investigated and many practitioners share different feelings about the different methods without a thorough review of the real influence on the outcome of the optimization, neither in terms of results or in terms of cost.

The students should build a benchmark for the methods, that is an optimization problem which well-posedness and conditioning will be at least numerically investigated. It is of great interest to find variants of the methods above that not only solve the problem of optimization but also reduce the overall cost of optimization while preserving the smoothness of the shape at each iteration of the optimization process.
These are challenges that need to be addressed if such methods should one day become standards in industrial applications.

The software will be provided by us but it would be necessary that the students have access to matlab + optimization-toolbox.