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When solving a PDE problem numerically, a certain mesh-refinement process isalways implicit, and very classically, mesh adaptivity is a very effectivemeans to accelerate grid convergence. Similarly, when optimizing a shape bymeans of an explicit geometrical representation, it is natural to seek for ananalogous concept of parameterization adaptivity. We propose here an adaptiveparameterization for three-dimensional optimum design in aerodynamics by usingthe so-called "Free-Form Deformation" approach based on 3D tensorial B\'ezierparameterization. The proposed procedure leads to efficient numericalsimulations with highly reduced computational costs.

Parameterization adaption for 3D shape optimization in aerodynamics