Publication: Structure-Exploiting Automatic Differentiation of Finite Element Discretizations
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Structure-Exploiting Automatic Differentiation of Finite Element Discretizations

- incollection -
 

Author(s)
P. Stumm , A. Walther , J. Riehme , U. Naumann

Published in
Advances in Automatic Differentiation

Editor(s)
Christian H. Bischof, H. Martin Bücker, Paul D. Hovland, Uwe Naumann, J. Utke

Year
2008

Publisher
Springer

Abstract
A common way to solve PDE constrained optimal control problems by automatic differentiation (ad) is the full black box approach. This technique may fail because of the large memory requirement. In this paper we present two alternative approaches. First, we exploit the structure in time yielding a reduced memory requirement. Second, we additionally exploit the structure in space by providing derivatives on a reference finite element. This approach reduces the memory requirement once again compared to the exploitation in time. We present numerical results for both approaches, where the derivatives are determined by the ad-enabled NAGWare Fortran compiler.

Cross-References
Bischof2008AiA

AD Tools
NAGWare Fortran 95

BibTeX
@INCOLLECTION{
         Stumm2008SEA,
       author = "P. Stumm and A. Walther and J. Riehme and U. Naumann",
       title = "Structure-Exploiting Automatic Differentiation of Finite Element Discretizations",
       doi = "10.1007/978-3-540-68942-3_30",
       booktitle = "Advances in Automatic Differentiation",
       crossref = "Bischof2008AiA",
       publisher = "Springer",
       editor = "Christian H. Bischof and H. Martin B{\"u}cker and Paul D. Hovland and Uwe
         Naumann and J. Utke",
       isbn = "978-3-540-68935-5",
       issn = "1439-7358",
       year = "2008",
       pages = "339--350",
       ad_tools = "NAGWare Fortran 95",
       abstract = "A common way to solve PDE constrained optimal control problems by automatic
         differentiation (AD) is the full black box approach. This technique may fail because of the large
         memory requirement. In this paper we present two alternative approaches. First, we exploit the
         structure in time yielding a reduced memory requirement. Second, we additionally exploit the
         structure in space by providing derivatives on a reference finite element. This approach reduces the
         memory requirement once again compared to the exploitation in time. We present numerical results for
         both approaches, where the derivatives are determined by the AD-enabled NAGWare Fortran compiler."
}


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