Aerodynamic Shape Optimization Using First and Second Order Adjoint and Direct Approaches

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Adjoint-based constrained topology optimization for viscous flows, including heat transfer (2013, methodology): “…and Frank 1991, Burgreen and Baysal 1996, Elliot and Peraire 1996, Giles and Pierce 1997) or continuous form (Pironneau 1974, Jameson 1988, Anderson and Venkatakrishnan 1997, Papadimitriou and Giannakoglou 2008) has been extensively used for solving shape optimization problems in fluid mechanics.”
Aerodynamic shape optimization for minimum robust drag and lift reliability constraint (2016, methodology): “In that case the derivatives dF dbi are computed by the expression [38, 4,31]”
Simultaneous identification of moving masses and structural damage (2010, methodology): “The formulation based on (37) and (35) allows the discrete adjoint method to be used (Haftka and Gürdal 1992), which is quicker by one order of magnitude in comparison to the standard direct differentiation method (Papadimitriou and Giannakoglou 2008).”