  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.
