Details
| Original language | English |
|---|---|
| Pages (from-to) | 5884-5906 |
| Number of pages | 23 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 123 |
| Issue number | 23 |
| Early online date | 5 Aug 2022 |
| Publication status | Published - 9 Nov 2022 |
Abstract
This article presents an efficient numerical algorithm to compute eigenvalues of stochastic problems. The proposed method represents stochastic eigenvectors by a sum of the products of unknown random variables and deterministic vectors. Stochastic eigenproblems are thus decoupled into deterministic and stochastic analyses. Deterministic vectors are computed efficiently via a few number of deterministic eigenvalue problems. Corresponding random variables and stochastic eigenvalues are solved by a reduced-order stochastic eigenvalue problem that is built by deterministic vectors. The computational effort and storage of the proposed algorithm increase slightly as the stochastic dimension increases. It can solve high-dimensional stochastic problems with low computational effort, thus the proposed method avoids the curse of dimensionality with great success. Numerical examples compared to existing methods are given to demonstrate the good accuracy and high efficiency of the proposed method.
Keywords
- curse of dimensionality, high-dimensional problems, reduced-order equations, stochastic finite element method, structural stochastic eigenvalues
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Engineering(all)
- General Engineering
- Mathematics(all)
- Applied Mathematics
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In: International Journal for Numerical Methods in Engineering, Vol. 123, No. 23, 09.11.2022, p. 5884-5906.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An efficient reduced-order method for stochastic eigenvalue analysis
AU - Zheng, Zhibao
AU - Beer, Michael
AU - Nackenhorst, Udo
N1 - Funding Information: The authors are grateful to the Alexander von Humboldt Foundation and the International Research Training Group 2657 (IRTG 2657) funded by the German Research Foundation (DFG) (Grant reference number 433082294). Open Access funding enabled and organized by Projekt DEAL. Funding Information: Alexander von Humboldt-Stiftung, Deutsche Stiftung Friedensforschung, Grant/Award Numbers: IRTG2657; 433082294The authors are grateful to the Alexander von Humboldt Foundation and the International Research Training Group 2657 (IRTG 2657) funded by the German Research Foundation (DFG) (Grant reference number 433082294). Open Access funding enabled and organized by Projekt DEAL.
PY - 2022/11/9
Y1 - 2022/11/9
N2 - This article presents an efficient numerical algorithm to compute eigenvalues of stochastic problems. The proposed method represents stochastic eigenvectors by a sum of the products of unknown random variables and deterministic vectors. Stochastic eigenproblems are thus decoupled into deterministic and stochastic analyses. Deterministic vectors are computed efficiently via a few number of deterministic eigenvalue problems. Corresponding random variables and stochastic eigenvalues are solved by a reduced-order stochastic eigenvalue problem that is built by deterministic vectors. The computational effort and storage of the proposed algorithm increase slightly as the stochastic dimension increases. It can solve high-dimensional stochastic problems with low computational effort, thus the proposed method avoids the curse of dimensionality with great success. Numerical examples compared to existing methods are given to demonstrate the good accuracy and high efficiency of the proposed method.
AB - This article presents an efficient numerical algorithm to compute eigenvalues of stochastic problems. The proposed method represents stochastic eigenvectors by a sum of the products of unknown random variables and deterministic vectors. Stochastic eigenproblems are thus decoupled into deterministic and stochastic analyses. Deterministic vectors are computed efficiently via a few number of deterministic eigenvalue problems. Corresponding random variables and stochastic eigenvalues are solved by a reduced-order stochastic eigenvalue problem that is built by deterministic vectors. The computational effort and storage of the proposed algorithm increase slightly as the stochastic dimension increases. It can solve high-dimensional stochastic problems with low computational effort, thus the proposed method avoids the curse of dimensionality with great success. Numerical examples compared to existing methods are given to demonstrate the good accuracy and high efficiency of the proposed method.
KW - curse of dimensionality
KW - high-dimensional problems
KW - reduced-order equations
KW - stochastic finite element method
KW - structural stochastic eigenvalues
UR - http://www.scopus.com/inward/record.url?scp=85135909396&partnerID=8YFLogxK
U2 - 10.1002/nme.7092
DO - 10.1002/nme.7092
M3 - Article
AN - SCOPUS:85135909396
VL - 123
SP - 5884
EP - 5906
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 23
ER -