Multilevel functional preconditioning for shape optimisation

摘要

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.