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

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Advances in Automatic Differentiation

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 64))

Summary

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.

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Authors and Affiliations

  1. Laboratoire de Physique et Mécanique des Matériaux, UMR 7554, Ile du Saulcy, 57045, Metz Cedex 1, France

    Isabelle Charpentier, Arnaud Lejeune & Michel Potier-Ferry

Authors
  1. Isabelle Charpentier
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  2. Arnaud Lejeune
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  3. Michel Potier-Ferry
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Editor information

Editors and Affiliations

  1. Institute for Scientific Computing, RWTH Aachen University, 52056, Aachen, Germany

    Christian H. Bischof  & H. Martin Bücker  & 

  2. Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S Cass Ave, Argonne, IL, 60439, USA

    Paul Hovland  & Jean Utke  & 

  3. Software and Tools for Computational Engineering, RWTH Aachen University, 52056, Aachen, Germany

    Uwe Naumann

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© 2008 Springer-Verlag Berlin Heidelberg

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Charpentier, I., Lejeune, A., Potier-Ferry, M. (2008). The Diamant Approach for an Efficient Automatic Differentiation of the Asymptotic Numerical Method. In: Bischof, C.H., Bücker, H.M., Hovland, P., Naumann, U., Utke, J. (eds) Advances in Automatic Differentiation. Lecture Notes in Computational Science and Engineering, vol 64. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68942-3_13

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