A Shape Optimization Algorithm for Interface Identification Allowing Topological Changes

  • Martin SiebenbornEmail author


In this work, we investigate a combination of classical optimization techniques from optimal control and a rounding strategy based on shape optimization for interface identification for problems constrained by partial differential equations. The goal is to identify the location of pollution sources in a fluid flow represented by a control that is either active or inactive. We use a relaxation of the binary problem on a coarse grid as initial guess for the shape optimization with higher resolution. The result is a computationally cheap method, where large shape deformations do not have to be performed. We demonstrate that our algorithm is, moreover, able to change the topology of the initial guess.


Shape optimization Interface identification Multigrid methods 

Mathematics Subject Classification

49Q10 35Q93 57N25 65M55 



This work has been partly supported by the German Research Foundation (DFG) within the priority program SPP 1648 “Software for Exascale Computing” under Contract No. Schu804/12-1 and the research training group 2126 “Algorithmic Optimization.”


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Universität HamburgHamburgGermany

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