Shape Optimization for the Mitigation of Coastal Erosion via Shallow Water Equations

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 to the obstacles. We model the propagation of waves towards the coastline, using two-dimensional shallow water equations. The obstacle's shape is optimized over an appropriate cost function to minimize the height and velocities of water waves along the shore, without relying on a finite-dimensional design space but based on shape calculus.