A shape optimization algorithm for interface identification allowing topological changes

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.

References in corpus (4)

• Efficient PDE constrained shape optimization based on Steklov-Poincaré type metrics
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Cited by in corpus (1)

• Shape optimization in $W^{1,\infty }$ with geometric constraints: a study in distributed-memory systems