Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map

Gianluigi Rozza; Toni Lassila; Andrea Manzoni

doi:10.1007/978-3-642-15337-2_28

Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map

Gianluigi Rozza^*
, Toni Lassila
, Andrea Manzoni

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Swiss Federal Institute of Technology Lausanne

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

31 Citations (Scopus)

Abstract

Reduced basis approximations for geometrically parametrized advection-diffusion equations are investigated. The parametric domains are assumed to be images of a reference domain through a piecewise polynomial map; this may lead to nonaffinely parametrized diffusion tensors that are treated with an empirical interpolation method. An a posteriori error bound including a correction term due to this approximation is given. Results concerning the applied methodology and the rigor of the corrected error estimator are shown for a shape optimization problem in a thermal flow.

Original language	English
Title of host publication	Spectral and High Order Methods for Partial Differential Equations - Selected Papers from the ICOSAHOM'09 Conference
Pages	307-315
Number of pages	9
Volume	76 LNCSE
DOIs	https://doi.org/10.1007/978-3-642-15337-2_28
Publication status	Published - 2011
MoE publication type	A4 Conference publication
Event	International Conference on Spectral and High Order Methods - Trondheim, Norway Duration: 22 Jun 2009 → 26 Jun 2009 Conference number: 8

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	76 LNCSE
ISSN (Print)	1439-7358

Conference

Conference	International Conference on Spectral and High Order Methods
Abbreviated title	ICOSAHOM
Country/Territory	Norway
City	Trondheim
Period	22/06/2009 → 26/06/2009

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10.1007/978-3-642-15337-2_28

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Rozza, G., Lassila, T., & Manzoni, A. (2011). Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map. In Spectral and High Order Methods for Partial Differential Equations - Selected Papers from the ICOSAHOM'09 Conference (Vol. 76 LNCSE, pp. 307-315). (Lecture Notes in Computational Science and Engineering; Vol. 76 LNCSE). https://doi.org/10.1007/978-3-642-15337-2_28

Rozza, Gianluigi ; Lassila, Toni ; Manzoni, Andrea. / Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map. Spectral and High Order Methods for Partial Differential Equations - Selected Papers from the ICOSAHOM'09 Conference. Vol. 76 LNCSE 2011. pp. 307-315 (Lecture Notes in Computational Science and Engineering).

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abstract = "Reduced basis approximations for geometrically parametrized advection-diffusion equations are investigated. The parametric domains are assumed to be images of a reference domain through a piecewise polynomial map; this may lead to nonaffinely parametrized diffusion tensors that are treated with an empirical interpolation method. An a posteriori error bound including a correction term due to this approximation is given. Results concerning the applied methodology and the rigor of the corrected error estimator are shown for a shape optimization problem in a thermal flow.",

author = "Gianluigi Rozza and Toni Lassila and Andrea Manzoni",

year = "2011",

doi = "10.1007/978-3-642-15337-2\_28",

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volume = "76 LNCSE",

series = "Lecture Notes in Computational Science and Engineering",

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Rozza, G, Lassila, T & Manzoni, A 2011, Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map. in Spectral and High Order Methods for Partial Differential Equations - Selected Papers from the ICOSAHOM'09 Conference. vol. 76 LNCSE, Lecture Notes in Computational Science and Engineering, vol. 76 LNCSE, pp. 307-315, International Conference on Spectral and High Order Methods, Trondheim, Norway, 22/06/2009. https://doi.org/10.1007/978-3-642-15337-2_28

Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map. / Rozza, Gianluigi; Lassila, Toni; Manzoni, Andrea.
Spectral and High Order Methods for Partial Differential Equations - Selected Papers from the ICOSAHOM'09 Conference. Vol. 76 LNCSE 2011. p. 307-315 (Lecture Notes in Computational Science and Engineering; Vol. 76 LNCSE).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

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AB - Reduced basis approximations for geometrically parametrized advection-diffusion equations are investigated. The parametric domains are assumed to be images of a reference domain through a piecewise polynomial map; this may lead to nonaffinely parametrized diffusion tensors that are treated with an empirical interpolation method. An a posteriori error bound including a correction term due to this approximation is given. Results concerning the applied methodology and the rigor of the corrected error estimator are shown for a shape optimization problem in a thermal flow.

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Rozza G, Lassila T, Manzoni A. Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map. In Spectral and High Order Methods for Partial Differential Equations - Selected Papers from the ICOSAHOM'09 Conference. Vol. 76 LNCSE. 2011. p. 307-315. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-642-15337-2_28

Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map

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