When solving a PDE problem numerically, a certain mesh-refinement process is always implicit, and very classically, mesh adaptivity is a very effective means to accelerate grid convergence. Similarly, when optimizing a shape by means of an explicit geometrical representation, it is natural to seek for an analogous concept of parameterization adaptivity. We propose here an adaptive parameterization for three-dimensional optimum design in aerodynamics by using the so-called "Free-Form Deformation" approach based on 3D tensorial B\'ezier parameterization. The proposed procedure leads to efficient numerical simulations with highly reduced computational costs.
@article{arxiv.1509.03227,
title = {Parameterization adaption for 3D shape optimization in aerodynamics},
author = {Badr Abou El Majd},
journal= {arXiv preprint arXiv:1509.03227},
year = {2015}
}