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"
}