BibTeX
@ARTICLE{
         Bischof2005Eaa,
       author = "C. H. Bischof and H. M. B{\"u}cker and B. Lang and A. Rasch and E.
         Slusanschi",
       title = "Efficient and accurate derivatives for a software process chain in airfoil shape
         optimization",
       journal = "Future Generation Computer Systems",
       pages = "1333--1344",
       doi = "doi:10.1016/j.future.2004.11.002",
       abstract = "When using a Newton-based numerical algorithm to optimize the shape of an airfoil
         with respect to certain design parameters, a crucial ingredient is the derivative of the objective
         function with respect to the design parameters. In large-scale aerodynamics, the objective function
         is typically given by a computer program written in a high-level programming language such as
         Fortran or C, and numerical differentiation is commonly used to approximate the derivatives. For a
         particular two-dimensional airfoil design problem, we apply automatic differentiation instead to
         compute derivatives that are accurate up to machine precision. In automatic differentiation, a given
         program is transformed into another program capable of computing the original function together with
         its derivatives. In the problem at hand, the objective function consists of a sequence of programs:
         a MATLAB program followed by two Fortran~77 programs. It is shown how automatic differentiation is
         applied to a sequence of programs while keeping the computational complexity within reasonable
         limits. The derivatives computed by automatic differentiation are compared with approximations based
         on divided differences.",
       year = "2005",
       volume = "21",
       number = "8",
       ad_area = "Computational Fluid Dynamics",
       ad_tools = "ADIFOR, ADiMat"
}