{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T04:37:37Z","timestamp":1787373457857,"version":"build-2736575974"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"name":"Landesforschungsforderungs","award":["LFF-GK11"],"award-info":[{"award-number":["LFF-GK11"]}]},{"name":"ShapeOptCompMat","award":["ACID 44171"],"award-info":[{"award-number":["ACID 44171"]}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GRK 2583"],"award-info":[{"award-number":["GRK 2583"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,4,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>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.<\/jats:p>","DOI":"10.1137\/22m1494609","type":"journal-article","created":{"date-parts":[[2023,4,7]],"date-time":"2023-04-07T04:15:22Z","timestamp":1680840922000},"page":"B231-B251","source":"Crossref","is-referenced-by-count":6,"title":["A Scalable Algorithm for Shape Optimization with Geometric Constraints in Banach Spaces"],"prefix":"10.1137","volume":"45","author":[{"given":"Peter Marvin","family":"M\u00fcller","sequence":"first","affiliation":[{"name":"Institute for Fluid Dynamics and Ship Theory, Hamburg University of Technology, Hamburg, Germany 21073."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0420-4230","authenticated-orcid":true,"given":"Jos\u00e9","family":"Pinz\u00f3n","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hamburg University, Hamburg, Germany 20146."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas","family":"Rung","sequence":"additional","affiliation":[{"name":"Institute for Fluid Dynamics and Ship Theory, Hamburg University of Technology, Hamburg, Germany 21073."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5716-5680","authenticated-orcid":true,"given":"Martin","family":"Siebenborn","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hamburg University, Hamburg, Germany 20146."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,4,7]]},"reference":[{"key":"ref1","unstructured":"Kitware, The Visualization Toolkit, https:\/\/vtk.org."},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/bs.hna.2020.10.004"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.09.032"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620320706"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012994278213"},{"key":"ref6","series-title":"Internat. 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