  Adjoint-based shape optimization most often relies on Eulerian flow field
formulations. However, since Lagrangian particle methods are the natural choice
for solving sedimentation problems in oceanography, extensions to the
Lagrangian framework are desirable. For the mitigation of coastal erosion, we
perform shape optimization for fluid flows, that are described by Lagrangian
shallow water equations and discretized via smoothed particle hydrodynamics.
The obstacle's shape is hereby optimized over an appropriate cost function to
minimize the height of water waves along the shoreline based on shape calculus.
Theoretical results will be numerically verified by exploring different
scenarios.
