Publications

Gradient-based optimizers can solve optimization problems with more than one thousand design variables. These optimizers require rapid and accurate derivative computation for efficient performance. For coupled multidisciplinary systems, implicit analytic methods (e.g., the adjoint method) offer the best computational efficiency for derivative computation. These methods first compute the partial derivatives of the subsystems (or disciplines) and then solve a linear system to obtain the system-level coupled derivatives. Solving this linear system is computationally intensive, so an efficient linear solver setup is critical. We propose new hierarchical linear solver strategies to accelerate derivative computations for problems with a specific structure. This includes problems with a high degree of embarrassingly parallel computations, such as trajectory optimization and optimization under uncertainty. Our strategies hide subsystem-level states and residuals from the system-level linear system. Users can independently choose linear solution strategies at the subsystem and system levels to achieve the fastest overall derivative computation. Our approach also dramatically shrinks the size and computational cost of the system-level linear system by doing more work at the subsystem level. This paper discusses when and why the proposed strategies are advantageous. We demonstrate the derivative accelerations on aircraft design optimization problems, which couple an aerostructural model, trajectory, propulsion model, and mission simulation. The proposed strategy computes derivatives up to 10 times faster than existing methods.