D. I. Papadimitriou and K. C. Giannakoglou Third-order sensitivity analysis for robust aerodynamic design using continuous adjoint International Journal for Numerical Methods in Fluids 71
An objective function for robust design problems includes the mean value and standard deviation of the shape performance, that is first-order and second-order derivatives with respect to the environmental variables, if second-order Taylor expansion is used. Working with gradient-based methods, this function should be differentiated with respect to the design variables. A method, based on the continuous adjoint and direct differentiation, for computing these third-order mixed derivatives is presented with applications in ducts and turbomachinery cascades.
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