One-shot Airfoil Optimisation with various strategies
by
A. Dervieux
INRIA, Sophia-Antipolis
Coauthors: Ch. Held

Adjoint methods allow to amplify the power of optimisation loops in aerodynamical departments. Indeed, sensitivy with respect to a large number of parameters is affordable, allowing a larger family of shapes and then a better optimisation. In the adjoint approach, each optimisation iteration has a (CPU) cost not much larger (let us say a factor 2-5) than the cost of one analysis, independantly of the number of parameters. For a rather coarse optimisation, just a few iterations of optimisation may produce sufficient results. Of course, for a very accurate optimisation with n parameters, n optimisation steps can be necessary for stiff cases. The resulting cost is in all cases much larger than one analysis, which is (about) the cost of traditional inverse methods; now such inverse methods generally cannot apply to the optimisation problem. One-shot or simultaneous solution of optimality system is an option that is very similar to inverse approach. It consists in solving the set of three optimality equations by advancing simultaneously the state variable, the adjoint state, the (shape) parameters as a kind of free boundary problem. Another way more rustical to understand this is to consider that the gradient method is applied but with only unperfect convergence of state and adjoint.

One-shot, Multi-level, adjoint:

Iteration on shape parameters may turn stiffer with a larger number of parameters. We concentrate on mesh-based parameters (the unknowns are essentially the position of boundary nodes) and choose as a crucial ingredient the application of a multi-level (or hierarchical) strategy in which a coarse level rely on every two nodes.

One-shot, Multi-level, divided-differences:

Another novelty in our approaches is the adaption of a one-shot multi-level algorithm to the case where we do not have an adjoint. Divided differences are then applied, also in a one-shot mode.

http://homepages.feis.herts.ac.uk/~comqun/AD2000/Ext_Abstracts/dervieux.ps

Date received: February 21, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cads-92.