2014/12/14 by Christian Leithäuser, Leithäuser, Christian, René Pinnau +3
Computer Science · Engineering · Mathematics · #30C20 #49J27 #49Q10 #76B75 #90C90 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #FOS: Mathematics #Optimization and Control (math.OC) #Topology Optimization in Engineering #math.OC #msc:30C20 #msc:49J27 #msc:49Q10 #msc:76B75 #msc:90C90
paper · pdf · doi:10.48550/arxiv.1412.4350
arxiv created 2014/12/14 · openalex publication_date 2014/12/14 · arxiv updated 2014/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal pull-back. The shape dependence is then hidden in a conformal parameter, which appears as a coefficient in the differential operators. The problem on the reference domain can be discretized, leading to an NLP which can be handled using existing solvers. Furthermore, we deal with the question how constraints on the conformal parameter can be used to preserve characteristic features of the geometry. We introduce this approach with the help of a Stokes flow, where the task is finding a shape such that the wall shear stress is uniformly close to some given target.