Publication: Efficient and accurate derivatives for a software process chain in airfoil shape optimization
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Efficient and accurate derivatives for a software process chain in airfoil shape optimization

- Article in a journal -
 

Area
Computational Fluid Dynamics

Author(s)
C. H. Bischof , H. M. Bücker , B. Lang , A. Rasch , E. Slusanschi

Published in
Future Generation Computer Systems

Year
2005

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.

AD Tools
ADIFOR, ADiMat

Related Applications
- Differentiation of the TFS Package

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"
}


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