Fluid dynamic shape optimization using self-adapting nonlinear extension operators with multigrid preconditioners

Abstract In this article we propose a scalable shape optimization algorithm which is tailored for large scale problems and geometries represented by hierarchically refined meshes. Weak scalability grid independent convergence achieved via combination of multigrid schemes the simulation PDEs quasi Newton methods on side. For purpose self-adapting, nonlinear extension operator proposed within framework method mappings. This demonstrated to identify critical regions in reference configuration where geometric singularities have arise or vanish. Thereby set admissible transformations adapted underlying situation. The performance example drag minimization an obstacle stationary, incompressible Navier–Stokes flow.