Frequency based preconditioning and smoothing for shape optimization

In this paper, we present a smoothing technique which can be understood as a Quasi-Newton method. The idea of this preconditioner is that it approximates the symbol of the inverse Hessian, which has smoothing behavior. This symbol is derived analytically for the Stokes equations and investigated numerically for a flow with a Reynolds number of 80. The resulting symbol is then approximated by differential operators, which will lead to a method similar to Sobolev Smoothing. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)