Multilevel functional Preconditioning for shape optimisation

Francois Courty
Alain Dervieux


Article in International Journal of CFD (44 pages)

Abstract: We study the application of a multi-level preconditioner to a practical optimal shape design problem. The preconditioner is based on the Bramble-Pasciak-Xu series. We extend it to the unstructured parametrization of 3D shapes by using the volume-agglomeration heuristics. The choice of the smoothing parameter is analysed from functional arguments. Application to the shape design for optimising aerodynamic and sonic boom performances of a wing is demonstrated.

Keywords: multilevel, optimal shape design, partial differential equations, Computational Fluid Dynamics, finite element, unstructured mesh

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@article{CourtyDervieux06,
  author = {Courty, F. and Dervieux, A.},
  title = {Multilevel functional Preconditioning for shape optimisation},
  journal = {International Journal of CFD},
  Volume = 20,
  Number = 7,
  pages = "481-490",
  year = 2006
}