Anisotropic multi-element polynomial chaos expansion for high-dimensional non-linear structural problems

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • A. A. Basmaji
  • A. Fau
  • J. H. Urrea-Quintero
  • M. M. Dannert
  • E. Voelsen
  • U. Nackenhorst

Externe Organisationen

  • École normale supérieure Paris-Saclay (ENS Paris-Saclay)
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Details

OriginalspracheEnglisch
Aufsatznummer103366
FachzeitschriftProbabilistic Engineering Mechanics
Jahrgang70
Frühes Online-Datum14 Sept. 2022
PublikationsstatusVeröffentlicht - Okt. 2022

Abstract

This work presents an hp-adaptive variant of multi-element polynomial chaos expansion (ME-gPCE), referred to as anisotropic multi-element polynomial chaos expansion (AME-gPCE). The main advantage of the proposed framework is that the basis functions of the local gPCE are selected adaptively within each local element. The p-adaptivity allows the order of the local uni-variate polynomials to be increased only for the dimensions associated with highly non-linear behaviour of the response surface, while the h-adaptivity allows the mesh refinement to be applied only where the local response surface behaves non-smoothly. Thus, the computational cost can be significantly reduced compared with standard methods, which opens the door to high-dimensional problems. The efficiency, accuracy and convergence of AME-gPCE are studied numerically and compared with the traditional ME-gPCE for non-linear structural analysis. It outperforms the traditional ME-gPCE for the elasto-plastic problem, considering the material proprieties as random variable and random fields.

ASJC Scopus Sachgebiete

Zitieren

Anisotropic multi-element polynomial chaos expansion for high-dimensional non-linear structural problems. / Basmaji, A. A.; Fau, A.; Urrea-Quintero, J. H. et al.
in: Probabilistic Engineering Mechanics, Jahrgang 70, 103366, 10.2022.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Basmaji AA, Fau A, Urrea-Quintero JH, Dannert MM, Voelsen E, Nackenhorst U. Anisotropic multi-element polynomial chaos expansion for high-dimensional non-linear structural problems. Probabilistic Engineering Mechanics. 2022 Okt;70:103366. Epub 2022 Sep 14. doi: 10.1016/j.probengmech.2022.103366
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title = "Anisotropic multi-element polynomial chaos expansion for high-dimensional non-linear structural problems",
abstract = "This work presents an hp-adaptive variant of multi-element polynomial chaos expansion (ME-gPCE), referred to as anisotropic multi-element polynomial chaos expansion (AME-gPCE). The main advantage of the proposed framework is that the basis functions of the local gPCE are selected adaptively within each local element. The p-adaptivity allows the order of the local uni-variate polynomials to be increased only for the dimensions associated with highly non-linear behaviour of the response surface, while the h-adaptivity allows the mesh refinement to be applied only where the local response surface behaves non-smoothly. Thus, the computational cost can be significantly reduced compared with standard methods, which opens the door to high-dimensional problems. The efficiency, accuracy and convergence of AME-gPCE are studied numerically and compared with the traditional ME-gPCE for non-linear structural analysis. It outperforms the traditional ME-gPCE for the elasto-plastic problem, considering the material proprieties as random variable and random fields.",
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AU - Basmaji, A. A.

AU - Fau, A.

AU - Urrea-Quintero, J. H.

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AU - Voelsen, E.

AU - Nackenhorst, U.

N1 - Funding Information: The support of the German Research Foundation (DFG) an International Research Training Group IRTG 2657 grant 433082294 is gratefully acknowledged as well as the French–German University under the French–German doctoral college “Sophisticated Numerical and Testing Approaches” (SNTA), grant DFDK 04-19 . This work was supported by the compute cluster, which is funded by the Leibniz University of Hannover , the Lower Saxony Ministry of Science and Culture (MWK) and the German Research Foundation (DFG) .

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N2 - This work presents an hp-adaptive variant of multi-element polynomial chaos expansion (ME-gPCE), referred to as anisotropic multi-element polynomial chaos expansion (AME-gPCE). The main advantage of the proposed framework is that the basis functions of the local gPCE are selected adaptively within each local element. The p-adaptivity allows the order of the local uni-variate polynomials to be increased only for the dimensions associated with highly non-linear behaviour of the response surface, while the h-adaptivity allows the mesh refinement to be applied only where the local response surface behaves non-smoothly. Thus, the computational cost can be significantly reduced compared with standard methods, which opens the door to high-dimensional problems. The efficiency, accuracy and convergence of AME-gPCE are studied numerically and compared with the traditional ME-gPCE for non-linear structural analysis. It outperforms the traditional ME-gPCE for the elasto-plastic problem, considering the material proprieties as random variable and random fields.

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