Two Level Correction Algorithm for Parametric Shape Inverse Optimization

Jichao Zhao (1) , Badr Abou El Majd (2) , Jean Antoine Désidéri (3)

1 Auckland Bioengineering Institute
2 University Hassan II [Casablanca]
3 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences

Our efforts are mostly concentrated on improving the convergence rate of the numerical procedures both from the viewpoint of cost-efficiency and accuracy by handling the parametrization of the shape to be optimized. We 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 this paper, we analyse and demonstrate the efficiency of the two-level correction algorithm which is the basic block of a more general miltilevel strategy.

Mots clés: Parametric shape optimization — RAE2822 airfoil — Model problem — Multilevel algorithms — Optimum shape-design in aerodynamics.

Domaines: Analyse numérique [math.NA]

Jichao Zhao, Badr Abou El Majd, Jean Antoine Désidéri. Two Level Correction Algorithm for Parametric Shape Inverse Optimization. International Journal of Engineering and Mathematical Modelling, 2015, 2 (1), pp.17-30. ⟨hal-01132859⟩