Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics
Journal of Computational Physics
A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs
SIAM Journal on Scientific Computing
Modeling of two-phase flows with surface tension by finite pointset method (FPM)
Journal of Computational and Applied Mathematics
Adjoint-based aerodynamic shape optimization on unstructured meshes
Journal of Computational Physics
Meshfree Particle Methods
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The paper at hand presents a combination of optimal control approaches for PDEs with meshless discretizations. Applying a classical Lagrangian type particle method to 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.