Enhancing Response Correction Techniques by Adjoint Sensitivity

Utilization of adjoint sensitivity techniques allows us to obtain both the response and its derivatives with respect to the geometry and/or material parameters of the structure of interest with a relatively small extra computational cost (El Sabbagh et al. 2006). In electromagnetic simulations, the process of obtaining the derivatives may not require additional simulations to the simulation for obtaining the figures of merit (El Sabbagh et al. 2006). In computational fluid dynamics (CFD), the cost of obtaining the gradients is almost equivalent to one additional flow solution (Jameson 1988). In both cases, the cost of obtaining the derivatives is independent of the number of design variables. Needless to say, the addition of adjoint sensitivities to simulation-based design and optimization has been transformative. In this chapter, we illustrate how surrogate-based modeling and optimization using response correction techniques can be enhanced with adjoint sensitivities. In particular, we start by discussing how to incorporate derivative data into the surrogate modeling and optimization process. Then, we provide the formulations for adjoint-enhanced versions of space mapping (Chap. 6 ), manifold mapping (Chap. 6 ), and shape-preserving response prediction (Chap. 7 ). For each technique, we provide example applications involving simulation-based design of several complex engineering systems including filters, and transonic airfoils.