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

Introduction

As shown in the previous chapter, the ‘optimization based’ multigrid method brings efficiency in the convergence of the optimization problem. This helps in considerable reduction of the number of optimization iterations required by the one-shot pseudo-time-stepping method. Hence, it reduces the over-all cost of computation. Since practical aerodynamic shape optimization problems involve additional state constraints, these problems are more challenging, and also more demanding, than those discussed in the previous chapter. Any reduction of computational cost of these problems pose a great challenge, since achieving the optimality faster leads to loss of feasibility of the constraint. We extend the multigrid strategy for these problems in this chapter.