2nd European Workshop on Automatic Differentiation

Thursday November 17- Friday November 18, 2005

Whitworth Conference Centre

Cranfield University (Shrivenham Campus)

Defence Academy of the UK

Shrivenham, Swindon

Sebastian Schlenkrich  and Andrea  Walther

Differentianting Fixed Point Iterations with ADOL-C

Abstract:  Automatic Differentiation (AD) based on a sequential internal function representation requires an amount of memory proportional to the size of the computational graph. For iterative processes of uniform complexity this means that the memory requirement is proportional to the number of iterations. Especially for fixed point iterations this is not efficient, since it neglegts any structure of the problem.

We apply the concept of Reverse Accumulation by B. Christianson within the AD tool ADOL-C to compute gradients of fixed point iterations. Results for the CFD code TAUij (DLR Braunschweig) will be presented. Furthermore we give an idea how to incorporate the differentiation of fixed point iterations into ADOL-C to decrease the memory requirement and therefore increase the range of applications.

Slides: SchlenkrichNov05.pdf