A Scalable Algorithm for Shape Optimization with Geometric Constraints in Banach Spaces

This work develops an algorithm for PDE-constrained shape optimization based on Lipschitz transformations. Building previous in this field, the $p$-Laplace operator is utilized to approximate a descent method shapes. In particular, it shown how geometric constraints are algorithmically incorporated avoiding penalty terms by assigning them subproblem of finding suitable direction. A special focus placed scalability proposed methods large scale parallel computers via application multigrid solvers. The preservation mesh quality under deformations, where singularities have be smoothed or generated within process, also discussed. It that interaction hierarchically refined grids and can realized choice appropriate directions. performance demonstrated energy dissipation minimization fluid dynamics applications.