Invited Session Mon.3.MA 415

Monday, 15:15 - 16:45 h, Room: MA 415

Cluster 19: PDE-constrained optimization & multi-level/multi-grid methods [...]

Numerical methods in shape and topology optimization


Chair: Antoine Laurain



Monday, 15:15 - 15:40 h, Room: MA 415, Talk 1

Kevin Sturm
Shape optimization for an interface problem in linear elasticity for distortion compensation

Coauthors: Michael Hintermüller, Dietmar Hömberg


In this talk I will introduce a sharp interface model describing a workpiece made of steel. In the heat treatment of steel different phases e.g., martensite and pearlite can be produced in the workpiece. The goal of my work is to obtain a desired workpiece shape by controlling the final phase distribution. Therefore our control variables are sets and thus we have to consider a shape optimization problem. I will show how one can derive the shape derivative for this problem, which then can be used to solve the shape optimization problem approximately. Moreover, numerical results for different workpiece shapes in two dimensions will be presented.



Monday, 15:45 - 16:10 h, Room: MA 415, Talk 2

Volker H. Schulz
On the usage of the shape Hessian in aerodynamic shape optimization


The talk demonstrates how approximations of the shape Hessian can be profitably used to accelerate shape optimization strategies significantly in the application field of aerodynamics. However, at least theoretically, the shape Hessian is of less advantage than usual Hessians - essentially because there does not yet exist a Taylor series expansion in terms of the shape Hessian, and it tends to be nonsymmetric. In this talk, a new view on the shape Hessian is proposed in terms of an appropriate distance measure. Furthermore consequences for numerical implementations are explained.


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