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arXiv · 1711.02535

A shape optimization algorithm for interface identification allowing topological changes

Martin Siebenborn
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Abstract

In this work we investigate a combination of classical PDE constrained optimization methods and a rounding strategy based on shape optimization for the identification of interfaces. The goal is to identify radioactive regions in a groundwater 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 that does not have to perform large shape deformations. We demonstrate that our algorithm is moreover able to change the topology of the initial guess.

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Martin Siebenborn. 2017-11-07. A shape optimization algorithm for interface identification allowing topological changes. https://doi.org/10.1007/s10957-018-1279-4

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