

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 Newtonbased 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 largescale aerodynamics, the objective function is typically given by a computer program written in a highlevel programming language such as Fortran or C, and numerical differentiation is commonly used to approximate the derivatives. For a particular twodimensional 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 = "13331344",
doi = "doi:10.1016/j.future.2004.11.002",
abstract = "When using a Newtonbased 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 largescale aerodynamics, the objective function
is typically given by a computer program written in a highlevel programming language such as
Fortran or C, and numerical differentiation is commonly used to approximate the derivatives. For a
particular twodimensional 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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