## Shape Optimization in Aerodynamics

**Area:**Optimization

We consider an optimization problem for the complete design chain of an airfoil. Starting with a parameter vector, one has to perform a three step procedure to evaluate the desired objective: Generate a grid around the airfoil, compute the flow around the airfoil, and compute the objective. Applying a calculus-based optimization method, one has to provide derivatives for this complex process. In the present paper, we propose the advanced use of automatic differentiation to compute the required gradient information. For this purpose, we employ the method of Reverse Accumulation that yields 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.

**Related AD-Tool:**ADOL-C

**Reference:**

S. Schlenkrich, A. Walther, N. R. Gauger, R. Heinrich

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

Conference proceeding,

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

Conference proceeding,

*Modeling, Simulation and Optimization of Complex Processes -- Proceedings of 3rd HPSC 2006*, Springer, 2008**People involved:**

- Nicolas Gauger,

DLR Braunschweig and HU Berlin - Andrea Walther,

TU Dresden