Ecient Hessian Calculations using Automatic Dierentiation and the Adjoint Method

In this paper an efficient general algorithm to calculate the Hessian of a steady or unsteady functional of interest in the context of computational fluid dynamics is outlined, validated and applied to an aerodynamic optimization and to an extrapolation example. The successful extrapolation is then applied to approximate Monte Carlo simulations for artificial geometric uncertainty analysis. The presented optimization examples demonstrate that the combination of automatic differentiation and an adjoint method to calculate the Hessian of a steady or unsteady objective function, and thereby obtaining second order information, can be an efficient tool for optimization and uncertainty quantification.

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