Title
Automatic differentiation for solving nonlinear partial differential equations : an efficient operator overloading approach Automatic differentiation for solving nonlinear partial differential equations : an efficient operator overloading approach
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Basel ,
Subject
Mathematics
Source (journal)
Numerical algorithms. - Basel
Volume/pages
30(2002) :3-4 , p. 259-301
ISSN
1017-1398
ISI
000177838300003
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Abstract
By resorting to Automatic Differentiation (AD) users of nonlinear PDE solvers can be relieved from the extra work of linearising a nonlinear PDE system and at the same time improve on the computational efficiency. This paper describes the main AD techniques and discusses how the operator overloading approach of AD can be extended to eliminate the overhead generally incurred with operator overloading. A recent AD system FastDer++, specially designed for this purpose, is integrated into a Least Squares solver. The necessary modifications to the general FEM algorithms. Code fragments and timing results demonstrate that (1) integrating AD with nonlinear PDE solvers leads to highly flexible code with a close resemblance to the mathematical expression of the problem, (2) coding and debugging efforts are greatly reduced, and (3) the computational efficiency is improved.
E-info
https://repository.uantwerpen.be/docman/iruaauth/c37b97/3386757.pdf
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