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  4. A scalable algorithm for shape optimization with geometric constraints in Banach spaces
 
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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)
Müller, Peter Marvin  orcid-logo
Fluiddynamik und Schiffstheorie M-8  
Pinzón, Jose  
Rung, Thomas  orcid-logo
Fluiddynamik und Schiffstheorie M-8  
Siebenborn, Martin  
Department of Mathematics, Hamburg University
Institut
Fluiddynamik und Schiffstheorie M-8  
TORE-DOI
10.15480/882.4497
TORE-URI
http://hdl.handle.net/11420/13267
Journal
SIAM journal on scientific computing  
Volume
45
Issue
2
End Page
B251
Citation
SIAM journal on scientific computing 45 (2): B231-B251 (2023)
Publisher DOI
10.1137/22M1494609
Scopus ID
2-s2.0-85157971507
ArXiv ID
2205.01912
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
Funding(s)
Simulationsbasierte Entwurfsoptimierung dynamischer Systeme unter Unsicherheiten  
Modellierung, Simulation und Optimierung mit fluiddynamischen Anwendungen  
Lizenz
http://rightsstatements.org/vocab/InC/1.0/
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