Algorithmic aspects of multigrid methods for optimization in shape spaces
Optimization and Control
2021-04-12 v3
Abstract
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of discrete approximations of geometrical quantities, like the mean curvature, on a multigrid shape optimization algorithm with quasi-Newton updates is investigated. For the purpose of illustration, we consider a complex model for the identification of cellular structures in biology with minimal compliance in terms of elasticity and diffusion equations.
Cite
@article{arxiv.1611.05272,
title = {Algorithmic aspects of multigrid methods for optimization in shape spaces},
author = {Martin Siebenborn and Kathrin Welker},
journal= {arXiv preprint arXiv:1611.05272},
year = {2021}
}