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research
Parametric free-form shape design with PDE models and reduced basis method
Authors
Abbott
Agoshkov
+43 more
Almroth
Amoiralis
Barrault
Bazaraa
Brenner
de Boor
Deparis
Farin
Fink
Gianluigi Rozza
Giannakoglou
Grepl
Grepl
Gunzburger
Haslinger
Huynh
Lamousin
Maday
Mohammadi
Morris
Nguyen
Nguyen
Noor
Panton
Piegl
Porsching
Praveen
Prud’homme
Quarteroni
Quarteroni
Queipo
Rozza
Rozza
Rozza
Samareh
Sarakinos
Sederberg
Sokolowski
Thiyagarajan
Toni Lassila
Veroy
Zienkiewicz
Zienkiewicz
Publication date
1 January 2010
Publisher
'Elsevier BV'
Doi
Cite
Abstract
We present a coupling of the reduced basis methods and free-form deformations for shape optimization and design of systems modelled by elliptic PDEs. The free-form deformations give a parameterization of the shape that is independent of the mesh, the initial geometry, and the underlying PDE model. The resulting parametric PDEs are solved by reduced basis methods. An important role in our implementation is played by the recently proposed empirical interpolation method, which allows approximating the non-affinely parameterized deformations with affinely parameterized ones. These ingredients together give rise to an efficient online computational procedure for a repeated evaluation design environment like the one for shape optimization. The proposed approach is demonstrated on an airfoil inverse design problem. © 2010 Elsevier B.V
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Infoscience - École polytechnique fédérale de Lausanne
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