Figure 1: Aeroelastic optimization of ARW-2 wing in the transonic regime
This project focuses on efficiently solving repeated analyses problems, particularly those encountered in design optimization. The approach taken is to use information computed at previous optimization iterations to accelerate convergence of the iterative solver used to compute the state and direct/adjoint sensitivities.

For more information:
Kevin Carlberg

Optimization techniques have become indispensable tools for myriad applications, including design, structural damage detection, and inverse problems. However, executing an optimization procedure can be prohibitively expensive, as it incurs repeated analyses of a high- fidelity (e.g. detailed finite element or finite volume) model of the physical system in different configurations (figure 1).

To this end, this project is focused on developing a framework for decreasing the cost of such repeated analyses while guaranteeing the satisfaction of any accuracy requirement. This framework is driven by two principles: exploit data from previous analyses as much as possible during future analyses, and accelerate convergence of new analyses using this data. The first principle is achieved by computing a proper orthogonal decomposition (POD) basis that optimally represents the state and sensitivity vectors computed at previous optimization steps.

To meet requirements of the second principle, a fast POD-based iterative solver is used. This solver employs the POD basis to accelerate convergence of the iterative solver used to evaluate the high-fidelity model. This approach guarantees cost savings because the POD basis can only accelerate convergence. Furthermore, the satisfaction of accuracy requirements is promised because the iterative method can continue to iterate until these requirements are met. When this framework is used, the high-fidelity model becomes less computationally expensive to evaluate as the optimization progresses (figure 2). This is due to the increase in size of the dataset and therefore continual improvement in quality of the POD basis.


Figure 2: Framework as applied to a gradient-based optimization problem. Circle size is proportional to computational cost, and the black lines represent the optimization trajectory.