Adaptive path-following primal dual interior point methods for shape optimization of linear and nonlinear Stokes flow problems

  • We are concerned with structural optimization problems in CFD where the state variables are supposed to satisfy a linear or nonlinear Stokes system and the design variables are subject to bilateral pointwise constraints. Within a primal-dual setting, we suggest an all-at-once approach based on interior-point methods. The discretization is taken care of by Taylor-Hood elements with respect to a simplicial triangulation of the computational domain. The efficient numerical solution of the discretized problem relies on adaptive path-following techniques featuring a predictor-corrector scheme with inexact Newton solves of the KKT system by means of an iterative null-space approach. The performance of the suggested method is documented by several illustrative numerical examples.

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Metadaten
Author:Ronald H. W. HoppeGND, Christopher LinsenmannGND, Harbir AntilGND
URN:urn:nbn:de:bvb:384-opus4-4373
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/543
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2007-18)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Contributing Corporation:Department of Mathematics, University of Houston
Release Date:2007/07/02
Tag:shape optimization; Stokes flow; interior point methods; adaptive path following
GND-Keyword:Deterministische Optimierung; Innere-Punkte-Methode; Gestaltoptimierung; Numerische Strömungssimulation
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik