Reproducing kernel Hilbert spaces and variable metric algorithms in PDE constrained shape optimisation
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2244 | |
dc.contributor.author | Eigel, Martin | |
dc.contributor.author | Sturm, Kevin | |
dc.date.accessioned | 2016-12-13T10:46:59Z | |
dc.date.available | 2019-06-28T08:01:58Z | |
dc.date.issued | 2016 | |
dc.description.abstract | In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape optimisation problems. We show that radial kernels provide convenient formulas for the shape gradient that can be efficiently used in numerical simulations. The shape gradients associated with radial kernels depend on a so called smoothing parameter that allows a smoothness adjustment of the shape during the optimisation process. Besides, this smoothing parameter can be used to modify the movement of the shape. The theoretical findings are verified in a number of numerical experiments. | |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/3116 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/1657 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.subject.ddc | 510 | |
dc.subject.other | Shape optimization | eng |
dc.subject.other | reproducing kernel Hilbert spaces | eng |
dc.subject.other | gradient method | eng |
dc.subject.other | variable metric | eng |
dc.subject.other | radial kernels | eng |
dc.title | Reproducing kernel Hilbert spaces and variable metric algorithms in PDE constrained shape optimisation | |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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