Optimal design of stationary flow problems by path-following interior-point methods
- We consider the numerical solution of structural optimization problems in CFD where the state variables are supposed to satisfy a linear or nonlinear Stokes system and the design variables are subject to bilateral pointwise constraints. Within a primal-dual setting, we suggest an all-at-once approach based on interior-point methods. The discretization is taken care of by Taylor-Hood elements with respect to a simplicial triangulation of the computational domain. The efficient numerical solution of the discretized problem relies on path-following techniques, namely a continuation method with an adaptive choice of the continuation step size and a long-step path-following algorithm. The performance of the suggested methods is documented by several illustrative numerical examples.
