Adjoint-based optimal control using meshfree discretizations

The paper at hand presents a combination of optimal control approaches for PDEs with meshless discretizations. Applying a classical Lagrangian type particle method 10 optimization problems with hyperbolic constraints, several adjoint-based strategies differing in the sequential order of optimization and discretization of the Lagrangian or Eulerian problem formulation are proposed and compared. The numerical results confirm the theoretically predicted independence principle of the optimization approaches and show the expected convergence behavior. Moreover, they exemplify the superiority of meshless methods over the conventional mesh-based approaches for the numerical handling and optimization of problems with time-dependent geometries and freely moving boundaries.