Multigrid One-Shot Pseudo-Time-Stepping Method for Aerodynamic Shape Optimization

Introduction

In all the applications mentioned in earlier Chapters 6-9, the cost of computation is reduced drastically in comparison to the traditional gradient methods. However, the number of optimization iterations is comparatively large since we update the design parameters after each time-step of the state and costate solver. Therefore, additional computational overhead due to, for example, grid generation, surface parameterization, etc., is high, specially for problems in 3D, since they are to be performed in each optimization iteration. In this paper we use a multigrid strategy to accelerate the optimization convergence.