Publication: The Diamant Approach for an Efficient Automatic Differentiation of the Asymptotic Numerical Method
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The Diamant Approach for an Efficient Automatic Differentiation of the Asymptotic Numerical Method

- incollection -
 

Author(s)
Isabelle Charpentier , Arnaud Lejeune , Michel Potier-Ferry

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
Based on high-order Taylor expansions, the asymptotic numerical method (ANM) is devoted to the solution of nonlinear partial differential equation (PDE) problems arising, for instance, in mechanics. Up to now, series were mainly handwritten and hand-coded. The note discusses the automation of the specific derivative computations involved in the ANM and presents the automatic differentiation (ad) approach Diamant. As any ad tool, Diamant is generic and may be used to differentiate the code of any differentiable behaviour law. Numerical performances, measured while solving a mechanical PDE problem, prove the efficiency of the Diamant approach.

Cross-References
Bischof2008AiA

AD Tools
Diamant

BibTeX
@INCOLLECTION{
         Charpentier2008TDA,
       title = "The Diamant Approach for an Efficient Automatic Differentiation of the Asymptotic
         Numerical Method",
       doi = "10.1007/978-3-540-68942-3_13",
       author = "Isabelle Charpentier and Arnaud Lejeune and Michel Potier-Ferry",
       abstract = "Based on high-order Taylor expansions, the asymptotic numerical method (ANM) is
         devoted to the solution of nonlinear partial differential equation (PDE) problems arising, for
         instance, in mechanics. Up to now, series were mainly handwritten and hand-coded. The note discusses
         the automation of the specific derivative computations involved in the ANM and presents the
         automatic differentiation (AD) approach Diamant. As any AD tool, Diamant is generic and may be used
         to differentiate the code of any differentiable behaviour law. Numerical performances, measured
         while solving a mechanical PDE problem, prove the efficiency of the Diamant approach.",
       crossref = "Bischof2008AiA",
       pages = "139--149",
       booktitle = "Advances in Automatic Differentiation",
       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",
       ad_tools = "Diamant"
}


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