Efficient Hessian Calculation Using Automatic Differentiation

This paper outlines the basic formulation for Hessian calculation for a functional of interest for aerodynamic applications. Complete analysis of the order of the computational cost with the number of independent variables is also presented. An efficient implementation strategy using automatic differentiation packages is outlined. Finally, results are presented for a two dimensional airfoil code and compared with finite difference Hessian calculation. Comparison of quadratic extrapolation of a functional of interest with the adjoint corrected linear extrapolation is also presented.