Title
Efficient operator overloading AD for solving nonlinear PDEs Efficient operator overloading AD for solving nonlinear PDEs
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
bookPart
Publication
Berlin :Springer, [*]
Subject
Mathematics
Computer. Automation
Source (book)
3rd International Conference on Automatic Differentiation, June, 2000, Côte d'Azur, France
ISBN - Hoofdstuk
0-387-95305-1
ISI
000176144500019
Carrier
E
Target language
English (eng)
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 [84] and ADOL-C [242, 243]. An application is discussed which dramatically reduces the cost of solver development.
E-info
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