TY - JOUR

T1 - Anisotropic multi-element polynomial chaos expansion for high-dimensional non-linear structural problems

AU - Basmaji, A. A.

AU - Fau, A.

AU - Urrea-Quintero, J. H.

AU - Dannert, M. M.

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) .

PY - 2022/10

Y1 - 2022/10

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.

AB - 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.

KW - Anisotropic multi-element polynomial chaos expansion

KW - hp-adaptivity

KW - Multi-element polynomial chaos expansion

KW - Non-linear stochastic finite element method

KW - Polynomial chaos expansion

UR - http://www.scopus.com/inward/record.url?scp=85138831358&partnerID=8YFLogxK

U2 - 10.1016/j.probengmech.2022.103366

DO - 10.1016/j.probengmech.2022.103366

M3 - Article

AN - SCOPUS:85138831358

VL - 70

JO - Probabilistic Engineering Mechanics

JF - Probabilistic Engineering Mechanics

SN - 0266-8920

M1 - 103366

ER -