Publication: Efficient Operator Overloading AD for Solving Nonlinear PDEs
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Efficient Operator Overloading AD for Solving Nonlinear PDEs

- incollection -
 

Author(s)
Engelbert Tijskens , Herman Ramon , Josse De Baerdemaeker

Published in
Automatic Differentiation of Algorithms: From Simulation to Optimization

Editor(s)
George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann

Year
2002

Publisher
Springer

Abstract
By employing automatic differentiation (ad), solvers for nonlinear systems of PDEs can be developed which relieve the user from the extra work of linearising a nonlinear PDE system and at the same time improve performance. This is achieved by extending common ad techniques using operator overloading to take advantage of the fact that in a FEM/FD/FV framework, a limited number of functions and their partial derivatives with respect to the unknowns have to be evaluated many times. The extension is implemented in C++ for both forward and reverse modes, and compared to hand coded evaluation of derivatives and two state-of-the-art ad implementations, ADIC [Bischof1997AAE] and ADOL-C [Griewank1996ACA][Griewank1996APf]. An application is discussed which dramatically reduces the cost of solver development.

Cross-References
Corliss2002ADo

BibTeX
@INCOLLECTION{
         Tijskens2002EOO,
       author = "Engelbert Tijskens and Herman Ramon and De Baerdemaeker, Josse",
       title = "Efficient Operator Overloading {AD} for Solving Nonlinear {PDEs}",
       pages = "167--172",
       chapter = "19",
       crossref = "Corliss2002ADo",
       booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
       year = "2002",
}


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