Details
| Original language | English |
|---|---|
| Article number | 103299 |
| Journal | Probabilistic Engineering Mechanics |
| Volume | 69 |
| Publication status | Published - Jul 2022 |
Abstract
Sophisticated sampling techniques used for solving stochastic partial differential equations efficiently and robustly are still in a state of development. It is known in the scientific community that global stochastic collocation methods using isotropic sparse grids are very efficient for simple problems but can become computationally expensive or even unstable for non-linear cases. The aim of this paper is to test the limits of these methods outside of a basic framework to provide a better understanding of their possible application in terms of engineering practices. Specifically, the stochastic collocation method using the Smolyak algorithm is applied to finite element problems with advanced features, such as high stochastic dimensions and non-linear material behaviour. We compare the efficiency and accuracy of different unbounded sparse grids (Gauss–Hermite, Gauss–Leja and Kronrod–Patterson) with Monte Carlo simulations. The sparse grids are constructed using an open source toolbox provided by Tamellini et al.,
Keywords
- Karhunen–Loève expansion, Modified exponential autocorrelation function, Non-linear stochastic finite element method, Plasticity, Random fields, Sparse grids, Stochastic collocation method
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Engineering(all)
- Civil and Structural Engineering
- Energy(all)
- Nuclear Energy and Engineering
- Physics and Astronomy(all)
- Condensed Matter Physics
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
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In: Probabilistic Engineering Mechanics, Vol. 69, 103299, 07.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Investigations on the restrictions of stochastic collocation methods for high dimensional and nonlinear engineering applications
AU - Dannert, Mona M.
AU - Bensel, Fynn
AU - Fau, Amelie
AU - Fleury, Rodolfo M.N.
AU - Nackenhorst, Udo
N1 - Funding Information: This work has been partially funded by the German Research Foundation (DFG) during the priority program SPP 1886 ( NA330/12-1 ) which is gratefully acknowledged. The support of the French–German University is acknowledged 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, Germany , the Lower Saxony Ministry of Science and Culture (MWK), Germany and the German Research Foundation (DFG) .
PY - 2022/7
Y1 - 2022/7
N2 - Sophisticated sampling techniques used for solving stochastic partial differential equations efficiently and robustly are still in a state of development. It is known in the scientific community that global stochastic collocation methods using isotropic sparse grids are very efficient for simple problems but can become computationally expensive or even unstable for non-linear cases. The aim of this paper is to test the limits of these methods outside of a basic framework to provide a better understanding of their possible application in terms of engineering practices. Specifically, the stochastic collocation method using the Smolyak algorithm is applied to finite element problems with advanced features, such as high stochastic dimensions and non-linear material behaviour. We compare the efficiency and accuracy of different unbounded sparse grids (Gauss–Hermite, Gauss–Leja and Kronrod–Patterson) with Monte Carlo simulations. The sparse grids are constructed using an open source toolbox provided by Tamellini et al.,
AB - Sophisticated sampling techniques used for solving stochastic partial differential equations efficiently and robustly are still in a state of development. It is known in the scientific community that global stochastic collocation methods using isotropic sparse grids are very efficient for simple problems but can become computationally expensive or even unstable for non-linear cases. The aim of this paper is to test the limits of these methods outside of a basic framework to provide a better understanding of their possible application in terms of engineering practices. Specifically, the stochastic collocation method using the Smolyak algorithm is applied to finite element problems with advanced features, such as high stochastic dimensions and non-linear material behaviour. We compare the efficiency and accuracy of different unbounded sparse grids (Gauss–Hermite, Gauss–Leja and Kronrod–Patterson) with Monte Carlo simulations. The sparse grids are constructed using an open source toolbox provided by Tamellini et al.,
KW - Karhunen–Loève expansion
KW - Modified exponential autocorrelation function
KW - Non-linear stochastic finite element method
KW - Plasticity
KW - Random fields
KW - Sparse grids
KW - Stochastic collocation method
UR - http://www.scopus.com/inward/record.url?scp=85132341943&partnerID=8YFLogxK
U2 - 10.1016/j.probengmech.2022.103299
DO - 10.1016/j.probengmech.2022.103299
M3 - Article
AN - SCOPUS:85132341943
VL - 69
JO - Probabilistic Engineering Mechanics
JF - Probabilistic Engineering Mechanics
SN - 0266-8920
M1 - 103299
ER -