  Coastal erosion describes the displacement of land caused by destructive sea
waves, currents or tides. Major efforts have been made to mitigate these
effects using groins, breakwaters and various other structures. We try to
address this problem by applying shape optimization techniques on the
obstacles. A first approach models the propagation of waves towards the
coastline, using a 2D time-harmonic system based on the famous Helmholtz
equation in the form of a scattering problem. The obstacle's shape is optimized
over an appropriate cost function to minimize the height of water waves along
the shoreline, without relying on a finite-dimensional design space, but based
on shape calculus.
