Preconditioning the Pressure Tracking in Fluid Dynamics by Shape Hessian Information


DOI: 10.1007/s10957-008-9507-y

Cite this article as:
Eppler, K., Schmidt, S., Schulz, V. et al. J Optim Theory Appl (2009) 141: 513. doi:10.1007/s10957-008-9507-y


Potential flow pressure matching is a classical inverse design aerodynamic problem. The resulting loss of regularity during the optimization poses challenges for shape optimization with normal perturbation of the surface mesh nodes. Smoothness is not enforced by the parameterization but by a proper choice of the scalar product based on the shape Hessian, which is derived in local coordinates for starshaped domains. Significant parts of the Hessian are identified and combined with an aerodynamic panel solver. The resulting shape Hessian preconditioner is shown to lead to superior convergence properties of the resulting optimization method. Additionally, preconditioning gives the potential for level independent convergence.


Shape optimization Aerodynamic optimization Hadamard gradient Shape Hessian Preconditioning 

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Technical University DresdenDresdenGermany
  2. 2.University TrierTrierGermany
  3. 3.German Aerospace Center (DLR)BraunschweigGermany

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