Frequency based preconditioning and smoothing for shape optimization. Issue 1 (25th October 2016)

• Record Type: Journal Article
• Authors: Kusch, Jonas; Gauger, Nicolas R.; Müller, Siegfried; Schmidt, Stephan
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 16:Issue 1(2016)
• Page Start: 701
• Page End: 702
• Publication Date: 2016-10-25
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201610339
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: 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)