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 -