Publication: Differentiating Fixed Point Iterations with ADOL-C: Gradient Calculation for Fluid Dynamics
Introduction
Applications
Tools
Research Groups
Workshops
Publications
   List Publications
   Advanced Search
   Info
   Add Publications
My Account
About

Differentiating Fixed Point Iterations with ADOL-C: Gradient Calculation for Fluid Dynamics

- Part of a collection -
 

Area
Computational Fluid Dynamics

Author(s)
S. Schlenkrich , A. Walther , N. R. Gauger , R. Heinrich

Published in
Modeling, Simulation and Optimization of Complex Processes -- Proceedings of 3rd HPSC 2006

Editor(s)
H. -G. Bock, E. Kostina, H. X. Phu, R. Rannacher

Year
2008

Publisher
Springer

Abstract
The reverse mode of Automatic Differentiation (ad) allows the computation of gradients at a temporal complexity that is only a small multiple of the function evlauation itself. However, the memory requirement of the reverse mode in its basic form is proportional to the size of the computational graph of the function to be differentiated. Hence, for iterative processes consisting of iterations with uniform complexity this means that the memory requirement caused by the reverse mode of ad is proportional to the number of iterations. For fixed point iterations this is not efficient, since it neglegts any structure of the problem. The method of Reverse Accumulation proposes for linear converging iterations an alternative, iterative computation of the gradient. The iteration of the gradient converges with the same rate as the fixed point iteration itself. The memory requirement for this method is independent of the number of iterations. Hence, it is also independent of the desired accuracy. We integrate the concept of Reverse Accumulation within the ad tool ADOL-C to compute gradients of fixed point iterations. This appraoch decreases the memory requirement of the gradient calculation considerably resulting in an increased range of applications. Results for a large scale application based on the CFD code TAUij are presented.

AD Tools
ADOL-C

AD Theory and Techniques
Reverse Mode

Related Applications
- Shape Optimization in Aerodynamics

BibTeX
@INPROCEEDINGS{
         Schlenkrich2008DFP,
       title = "Differentiating Fixed Point Iterations with {ADOL-C}: Gradient Calculation for Fluid
         Dynamics",
       author = "S. Schlenkrich and A. Walther and N.R. Gauger and R. Heinrich",
       editor = "H.-G. Bock and E. Kostina and H.X. Phu and R. Rannacher",
       year = "2008",
       booktitle = "Modeling, Simulation and Optimization of Complex Processes -- Proceedings of 3rd
         HPSC 2006",
       pages = "499--508",
       publisher = "Springer",
       abstract = "The reverse mode of Automatic Differentiation (AD) allows the computation of
         gradients at a temporal complexity that is only a small multiple of the function evlauation itself.
         However, the memory requirement of the reverse mode in its basic form is proportional to the size of
         the computational graph of the function to be differentiated. Hence, for iterative processes
         consisting of iterations with uniform complexity this means that the memory requirement caused by
         the reverse mode of AD is proportional to the number of iterations. For fixed point iterations this
         is not efficient, since it neglegts any structure of the problem. The method of Reverse Accumulation
         proposes for linear converging iterations an alternative, iterative computation of the gradient. The
         iteration of the gradient converges with the same rate as the fixed point iteration itself. The
         memory requirement for this method is independent of the number of iterations. Hence, it is also
         independent of the desired accuracy. We integrate the concept of Reverse Accumulation within the AD
         tool ADOL-C to compute gradients of fixed point iterations. This appraoch decreases the memory
         requirement of the gradient calculation considerably resulting in an increased range of
         applications. Results for a large scale application based on the CFD code TAUij are presented.",
       ad_area = "Computational Fluid Dynamics",
       ad_tools = "ADOL-C",
       ad_theotech = "Reverse Mode"
}


back
  

Contact:
autodiff.org
Username:
Password:
(lost password)