Optimal design of stationary flow problems by path-following interior-point methods

  • We consider the numerical solution of 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 path-following techniques, namely a continuation method with an adaptive choice of the continuation step size and a long-step path-following algorithm. The performance of the suggested methods is documented by several illustrative numerical examples.

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Author:Harbir AntilGND, Ronald H. W. HoppeORCiDGND, Christopher Linsenmann
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/505
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2007-02)
Publishing Institution:Universität Augsburg
Contributing Corporation:Department of Mathematics, University of Houston
Release Date:2007/05/25
Tag:optimal design; primal-dual interior-point methods; adaptive continuation methods
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