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D ECENT efforts in the field of aerodynamic shape

~ ptimization(ASO) have yielded remarkable improvements in our ability to design shapes with certain types of optimal behavior. By leveraging concepts from control theory, the computational cost of traditional gradient-based optimization schemes can be substantially decreased via solution of an adjoint equation. This procedure effectively yields the gradient with respect to an arbitrary number of design variables with the cost of a single flow and adjoint solution. 1-3 The adjoint procedure ha. s undergone intensive scrutiny during the last few years and has matured to the point where both complex geometries and viscous flows are starting to be treated with reasonable confidence. 4-5

In spite of these great contributions, the application of the adjoint procedure has been limited to the computations confined to the fields of aerodynamic and structural design. The …