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Title: Inverse Subspace Iteration for Spectral Stochastic Finite Element Methods

Journal Article · · SIAM/ASA Journal on Uncertainty Quantification
DOI:https://doi.org/10.1137/140999359· OSTI ID:1418636
 [1];  [2]
  1. Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States)
  2. Univ. of Maryland, College Park, MD (United States)
+ Show Author Affiliations

We study random eigenvalue problems in the context of spectral stochastic finite elements. In particular, given a parameter-dependent, symmetric positive-definite matrix operator, we explore the performance of algorithms for computing its eigenvalues and eigenvectors represented using polynomial chaos expansions. We formulate a version of stochastic inverse subspace iteration, which is based on the stochastic Galerkin finite element method, and we compare its accuracy with that of Monte Carlo and stochastic collocation methods. The coefficients of the eigenvalue expansions are computed from a stochastic Rayleigh quotient. Our approach allows the computation of interior eigenvalues by deflation methods, and we can also compute the coefficients of multiple eigenvectors using a stochastic variant of the modified Gram-Schmidt process. The effectiveness of the methods is illustrated by numerical experiments on benchmark problems arising from vibration analysis.

Research Organization:
Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States)
Sponsoring Organization:
National Science Foundation (NSF); USDOE
Grant/Contract Number:
SC0009301; DMS1418754; DMS1521563.
OSTI ID:
1418636
Journal Information:
SIAM/ASA Journal on Uncertainty Quantification, Vol. 4, Issue 1; ISSN 2166-2525
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 8 works
Citation information provided by
Web of Science

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Cited By (2)

Stochastic collocation method for computing eigenspaces of parameter-dependent operators journal December 2022
Asymptotic convergence of spectral inverse iterations for stochastic eigenvalue problems preprint January 2017

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