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A scalable algorithm for shape optimization with geometric constraints in Banach spaces
Citation Link: https://doi.org/10.15480/882.4497
Publikationstyp
Journal Article
Date Issued
2023
Sprache
English
Author(s)
Department of Mathematics, Hamburg University
Institut
TORE-DOI
Volume
45
Issue
2
End Page
B251
Citation
SIAM journal on scientific computing 45 (2): B231-B251 (2023)
Publisher DOI
Scopus ID
ArXiv ID
Peer Reviewed
false
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.
Subjects
Shape optimization
Lipschitz transformations
p-Laplace
geometric multigrid
parallel computing
DDC Class
004: Informatik
530: Physik
600: Technik
620: Ingenieurwissenschaften
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