Model reduction and level set methods for shape optimization problems

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en Lassila, Toni 2012-08-28T11:47:33Z 2012-08-28T11:47:33Z 2010
dc.identifier.isbn 978-952-60-3402-7 (electronic)
dc.identifier.isbn 978-952-60-3401-0 (printed) #8195;
dc.description.abstract In this work two topics related to mathematical shape optimization are considered. Topological optimization methods need not know the correct topology (number of connected components and possible holes) of the optimal shape beforehand. Shape optimization can be performed by a topological gradient descent algorithm. Computational applications of topological optimization and level set based shape optimization involve the optimal damping of vibrating structures and an inverse problem of reconstructing a shape based on noisy interferogram measurements. For parametric shape optimization with partial differential constraints the model reduction approach of reduced basis methods is considered. In the reduced basis method a basis of snapshot solutions is used to construct a problem-dependent approximation space that has much smaller dimension than the underlying finite element approximations. The state constraints for optimization are then replaced with their reduced basis approximation, leading to efficient shape optimization methods. Computational examples involve the optimal engineering design of airfoils in potential and thermal flow. en
dc.format.extent Verkkokirja (366 KB, 31 s.)
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher Aalto-yliopiston teknillinen korkeakoulu en
dc.relation.ispartofseries Research reports / Helsinki University of Technology, Institute of Mathematics. A, 593 en
dc.relation.haspart [Publication 1]: Toni Lassila. 2009. Optimal damping of a membrane and topological shape optimization. Structural and Multidisciplinary Optimization, volume 38, number 1, pages 43-52. en
dc.relation.haspart [Publication 2]: Timo Eirola and Toni Lassila. 2009. Optimization of convex shapes: An approach to crystal shape identification. In: Xue-Cheng Tai, Knut Mørken, Marius Lysaker, and Knut-Andreas Lie (editors). Proceedings of the 2nd International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2009). Voss, Norway. 1-5 June 2009. Berlin, Heidelberg, Germany. Springer. Lecture Notes in Computer Science, volume 5567, pages 660-671. ISBN 978-3-642-02255-5. en
dc.relation.haspart [Publication 3]: Toni Lassila and Gianluigi Rozza. 2010. Parametric free-form shape design with PDE models and reduced basis method. Computer Methods in Applied Mechanics and Engineering, volume 199, numbers 23-24, pages 1583-1592. © 2010 Elsevier Science. By permission. en
dc.relation.haspart [Publication 4]: Gianluigi Rozza, Toni Lassila, and Andrea Manzoni. 2011. Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map. In: Jan S. Hesthaven and Einar M. Rønquist (editors). Spectral and High Order Methods for Partial Differential Equations. Selected Papers from the 8th International Conference on Spectral and High Order Methods (ICOSAHOM 2009). Trondheim, Norway. 22-26 June 2009. Berlin, Heidelberg, Germany. Springer. Lecture Notes in Computational Science and Engineering, volume 76, pages 307-315. ISBN 978-3-642-15336-5. © 2011 by authors and © 2011 Springer Science+Business Media. By permission. en
dc.relation.haspart [Publication 5]: Toni Lassila and Gianluigi Rozza. 2010. Reduced formulation of a steady fluid-structure interaction problem with parametric coupling. arXiv:1005.3384v1 [math.NA]. Previously published in: R. A. E. Mäkinen, P. Neittaanmäki, T. Tuovinen, and K. Valpe (editors). Proceedings of the 10th Finnish Mechanics Days. Jyväskylä, Finland. 3-4 December 2009. 10 pages. ISBN 978-951-39-3738-6. © 2010 by authors. en
dc.subject.other Mathematics
dc.title Model reduction and level set methods for shape optimization problems en
dc.type G5 Artikkeliväitöskirja fi Aalto-yliopiston teknillinen korkeakoulu fi
dc.contributor.department Matematiikan ja systeemianalyysin laitos fi
dc.contributor.department Department of Mathematics and Systems Analysis en
dc.subject.keyword shape optimization en
dc.subject.keyword topological optimization en
dc.subject.keyword level set method en
dc.subject.keyword model reduction en
dc.subject.keyword reduced basis method en
dc.subject.keyword partial differential equations en
dc.subject.keyword 35R35
dc.subject.keyword 49Q10
dc.subject.keyword 65K10
dc.identifier.urn URN:ISBN:978-952-60-3402-7
dc.type.dcmitype text en
dc.type.ontasot Väitöskirja (artikkeli) fi
dc.type.ontasot Doctoral dissertation (article-based) en
dc.contributor.supervisor Eirola, Timo, Prof.

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