BibTeX
@ARTICLE{
         Bischof2003Etf,
       author = "C. H. Bischof and H. M. B{\"u}cker and B. Lang and A. Rasch and J. W.
         Risch",
       title = "Extending the functionality of the general-purpose finite element package {SEPRAN} by
         automatic differentiation",
       journal = "International Journal for Numerical Methods in Engineering",
       pages = "2225--2238",
       abstract = "From an abstract point of view, a numerical simulation implements a mathematical
         function that produces some output from some given input. Derivatives (or sensitivities) of the
         function's output with respect to its input can be obtained---free from truncation error---by
         using a technique called automatic differentiation. Given a computer code in a high-level
         programming language like Fortran, C, or, C++, automatic differentiation generates another code
         capable of computing not only the original function but also its derivatives. Thus, the application
         of automatic differentiation significantly extends the functionality of a simulation package. For
         instance, automatic differentiation enables, in a completely mechanical fashion, the usage of
         derivative-based optimization algorithms where the evaluation of the objective function comprises
         some given large-scale engineering simulation. In this note, the automatic differentiation tool
         Adifor is used to transform the general purpose finite element package SEPRAN.\@ In doing so,
         we automatically translate the given 400,000 lines of Fortran~77 into a new program consisting of
         600,000 lines of Fortran~77. We compare our approach with a traditional approach based on numerical
         differentiation and quantify its advantages in terms of accuracy and computational efficiency for a
         standard fluid flow problem.",
       ad_tools = "ADIFOR",
       ad_theotech = "General",
       year = "2003",
       volume = "58",
       number = "14",
       doi = "10.1002/nme.942"
}