International audienceThe essential numerical features of multilevel strategies developed for parametric shape optimization are reviewed. These methods employ nested parameterization supports of either shape, or shape deformation, and the classical process of degree elevation resulting in exact geometrical data transfer from coarse to fine representations. The algorithms mimick classical multigrid strategies and are found very effective in terms of convergence acceleration. In particular, for a drag reduction problem involving a three-dimensional Eulerian transonic flow simulated by an unstructured-grid finite-volume method, the complete algorithm is found to be noticeably superior to the natural algorithm simply based on progressive degree elevation
