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978-3-8439-0880-1, Reihe Mathematik
Controllability of Shape-Dependent Operators and Constrained Shape Optimization for Polymer Distributors
147 Seiten, Dissertation Technische Universität Kaiserslautern (2013), Softcover, A5
This thesis deals with theoretical and numerical aspects of shape optimization for flow problems. In a first part we investigate the controllability of shape-dependent operators. We derive a characterization for the image space of a potential flow operator and draw a connection to its stagnation points. And we show approximate controllability for linearized shape-dependent operators based on the potential flow, Stokes flow and the instationary heat equation.
In a numerical part we introduce a new approach for shape optimization problems with state constraints and non differentiable cost functionals. We use conformal pull-back to reformulate the problem on a fixed reference domain. The resulting nonlinear problem can be discretized and solved using discrete optimization.
Finally, we consider the industrial problem of designing an optimal distributor geometry for spin packs as used in fiber production. The goal is to construct a geometry with a certain wall shear stress distribution. This problem is solved using classical L2 shape optimization.