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Efficient Operator Overloading AD for Solving Nonlinear PDEs-
incollection
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Author(s)
Engelbert Tijskens
, Herman Ramon
, Josse De Baerdemaeker
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Published in
Automatic Differentiation of Algorithms: From Simulation to Optimization
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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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