|
Title
|
|
|
|
Efficient operator overloading AD for solving nonlinear PDEs
| |
|
Author
|
|
|
|
| |
|
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. |
| |
|
Language
|
|
|
|
English
| |
|
Source (book)
|
|
|
|
3rd International Conference on Automatic Differentiation, June, 2000, Côte d'Azur, France
| |
|
Publication
|
|
|
|
Berlin
:
Springer
,
2002
| |
|
ISBN
|
|
|
|
0-387-95305-1
| |
|
Volume/pages
|
|
|
|
p. 167-172
| |
|
ISI
|
|
|
|
000176144500019
| |
|