Inverse Subspace Iteration for Spectral Stochastic Finite Element Methods

Sousedík, Bedřich; Elman, Howard C.

doi:10.1137/140999359

Inverse Subspace Iteration for Spectral Stochastic Finite Element Methods

Journal Article · Thu Feb 25 00:00:00 EST 2016 · SIAM/ASA Journal on Uncertainty Quantification

DOI:https://doi.org/10.1137/140999359· OSTI ID:1418636

Sousedík, Bedřich ^[1]; Elman, Howard C. ^[2]

Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States); US Dept. of Energy, Office of Scientific and Technical Information (OSTI)
Univ. of Maryland, College Park, MD (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States)

Sponsoring Organization:: National Science Foundation; USDOE

Grant/Contract Number:: SC0009301

OSTI ID:: 1418636

Journal Information:: SIAM/ASA Journal on Uncertainty Quantification, Journal Name: SIAM/ASA Journal on Uncertainty Quantification Journal Issue: 1 Vol. 4; ISSN 2166-2525

Publisher:: SIAMCopyright Statement

Country of Publication:: United States

Language:: English

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Cited By (2)

Stochastic collocation method for computing eigenspaces of parameter-dependent operators Grubišić, Luka; Saarikangas, Mikael; Hakula, Harri Numerische Mathematik, Vol. 153, Issue 1 https://doi.org/10.1007/s00211-022-01339-3	journal	December 2022
Asymptotic convergence of spectral inverse iterations for stochastic eigenvalue problems Hakula, Harri; Laaksonen, Mikael arXiv https://doi.org/10.48550/arxiv.1706.03558	preprint	January 2017

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