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arXiv ID: 2205.01912
Title: A scalable algorithm for shape optimization with geometric constraints in Banach spaces
Language: English
Authors: Müller, Peter Marvin  
Pinzón, Jose 
Rung, Thomas  
Siebenborn, Martin 
Keywords: Shape optimization; Lipschitz transformations; p-Laplace; geometric multigrid; parallel computing
Issue Date: 4-May-2022
Source: arXiv:2205.01912 (2022)
Abstract (english): 
This work develops an algorithm for PDE-constrained shape optimization based on Lipschitz transformations. Building on previous work in this field, the p-Laplace operator is utilized to approximate a descent method for Lipschitz shapes. In particular, it is shown how geometric constraints are algorithmically incorporated avoiding penalty terms by assigning them to the subproblem of finding a suitable descent direction. A special focus is placed on the scalability of the proposed methods for large scale parallel computers via the application of multigrid solvers. The preservation of mesh quality under large deformations, where shape singularities have to be smoothed or generated within the optimization process, is also discussed. It is shown that the interaction of hierarchically refined grids and shape optimization can be realized by the choice of appropriate descent directions. The performance of the proposed methods is demonstrated for energy dissipation minimization in fluid dynamics applications.
DOI: 10.15480/882.4497
Institute: Fluiddynamik und Schiffstheorie M-8 
Document Type: Preprint
Project: Simulationsbasierte Entwurfsoptimierung dynamischer Systeme unter Unsicherheiten 
Modellierung, Simulation und Optimierung mit fluiddynamischen Anwendungen 
Peer Reviewed: No
License: In Copyright In Copyright
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