Aerodynamic Shape Optimization using a Full and Adaptive Multilevel Algorithm

Badr Abou El Majd (1) , Regis Duvigneau (1) , Jean-Antoine Désidéri (1)

1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE

We are interested by the general problem consisting of minimizing a functional of a state field solution of a PDE state equation. In Particular in this work, we optimize a 3D wing shape immersed an in inviscid flow to reduce drag. Whence, each evaluation of the cost functional is computationally expensive. For improving the convergence rate of the optimization algorihm, we propose a multi-scale algorithm inspired from the Full Multi-Grid method [1], and referred to as the Full and Adaptive Multi-Level Optimum-Shape Algorithm (FAMOSA), originally defined in [5]. The proposed method include the following strategies: • The simplest scheme " one way up " by choosing the parametrization of Bézier type to construct a hierarchy of embedded parametric spaces, via the classical degree elevation process [3]. • V-cycle algorithm by using (on the coarse level) " perturbation " unknowns from the latest fine estimate, i.e deformation instead of shapes.

Mots clés: Partial-Differential Equations; Multi-Level; Numerical Shape Optimization; Compressible Aerodynamics; Euler equations

Domaines: Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]

Badr Abou El Majd, Regis Duvigneau, Jean-Antoine Désidéri. Aerodynamic Shape Optimization using a Full and Adaptive Multilevel Algorithm. ERCOFTAC Conference Design Optimization: Methods and Applications, Apr 2004, Canary Island, Spain. ⟨hal-01567729⟩