An efficient reduced-order method for stochastic eigenvalue analysis
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.
Details
- Organisationseinheit(en)
-
Institut für Risiko und Zuverlässigkeit
Institut für Baumechanik und Numerische Mechanik
Internationales GRK 2657: Methoden der Numerischen Mechanik in höheren Dimensionen
- Externe Organisation(en)
-
The University of Liverpool
Tongji University
- Typ
- Artikel
- Journal
- International Journal for Numerical Methods in Engineering
- Band
- 123
- Seiten
- 5884-5906
- Anzahl der Seiten
- 23
- ISSN
- 0029-5981
- Publikationsdatum
- 09.11.2022
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Numerische Mathematik, Allgemeiner Maschinenbau, Angewandte Mathematik
- Elektronische Version(en)
-
https://doi.org/10.1002/nme.7092 (Zugang:
Offen
)
