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SHAPE OPTIMIZATION FOR FREE BOUNDARY PROBLEMS

  • In this paper three different formulations of a Bernoulli type free boundary problem are discussed. By analyzing the shape Hessian in case of matching data it is distinguished between well-posed and ill-posed formulations. A nonlinear Ritz-Galerkin method is applied for discretizing the shape optimization problem. In case of well-posedness existence and convergence of the approximate shapes isIn this paper three different formulations of a Bernoulli type free boundary problem are discussed. By analyzing the shape Hessian in case of matching data it is distinguished between well-posed and ill-posed formulations. A nonlinear Ritz-Galerkin method is applied for discretizing the shape optimization problem. In case of well-posedness existence and convergence of the approximate shapes is proven. In combination with a fast boundary element method efficient first and second order shape optimization algorithms are obtained.show moreshow less

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Metadaten
Document Type:Conference Proceeding
Author: Helmut Harbrecht, K. Eppler
DOI (Cite-Link):https://doi.org/10.25643/bauhaus-universitaet.2850Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170314-28508Cite-Link
URL:http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
ISSN:1611-4086
Editor: Klaus GürlebeckGND, Carsten KönkeORCiDGND
Language:English
Date of Publication (online):2017/03/04
Date of first Publication:2010/07/14
Release Date:2017/03/14
Publishing Institution:Bauhaus-Universität Weimar
Creating Corporation:Bauhaus-Universität Weimar
Institutes and partner institutions:Bauhaus-Universität Weimar / In Zusammenarbeit mit der Bauhaus-Universität Weimar
Pagenumber:8
Tag:Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
GND Keyword:Angewandte Informatik; Angewandte Mathematik; Architektur <Informatik>; Computerunterstütztes Verfahren
Dewey Decimal Classification:000 Informatik, Informationswissenschaft, allgemeine Werke / 000 Informatik, Wissen, Systeme
500 Naturwissenschaften und Mathematik / 510 Mathematik
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
56 Bauwesen / 56.03 Methoden im Bauingenieurwesen
Collections:Bauhaus-Universität Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar, 18. 2009
Licence (German):License Logo Creative Commons 4.0 - Namensnennung-Nicht kommerziell (CC BY-NC 4.0)