Multilevel functional preconditioning for shape optimisation

Abstract

We study the application of a multi-level preconditioner to a practical optimal shape design problem. The preconditioner is based on the Bramble-Pasciak-Xu (BPX) series. We extend it to the unstructured parametrization of 3D shapes by using the volume–agglomeration heuristics. The choice of the smoothing parameter is analysed from functional arguments. Application to the shape design for optimising aerodynamic and sonic boom performances of a wing is demonstrated.