Optimum shape design through multilevel gradient-based method using Bézier parametrisation

In the context of aerodynamic optimum shape design, the evaluation of the cost functional requires the solution of the governing flow equations, and thus, each optimisation iteration is characterised by a high computational cost if problems of industrial interest are considered. Thus, the improvement of optimisation algorithm efficiency is a crucial point. In [1] a multilevel strategy considering shape grid-point coordinates as design variables has been defined to make the convergence rate of the gradient-based method almost independent of the number of control parameters. The idea of a multilevel strategy for shape optimisation has also been used in [2], but, in a context slightly different.