Adaptive Path Following Primal Dual Interior Point Methods for Shape Optimization of Linear and Nonlinear Stokes Flow Problems

Authors:
Ronald H. Hoppe;Christopher Linsenmann;Harbir Antil
Affiliations:
Department of Mathematics, University of Houston, and Institute for Mathematics, University of Augsburg,;Department of Mathematics, University of Houston, and Institute for Mathematics, University of Augsburg,;Department of Mathematics, University of Houston,
Venue:
Large-Scale Scientific Computing
Year:
2009

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Abstract

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.