Asymptotic convergence of spectral inverse iterations for stochastic eigenvalue problems

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Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2019-01-01
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Mcode
Degree programme
Language
en
Pages
1-33
Series
Numerische Mathematik
Abstract
We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought from a finite dimensional space formed as the tensor product of the approximation space for the underlying stochastic function space, and the approximation space for the underlying spatial function space. Sparse polynomial approximation is employed to obtain the first one, while classical finite elements are employed to obtain the latter. An error analysis is presented for the asymptotic convergence of the spectral inverse iteration to the smallest eigenvalue and the associated eigenvector of the problem. A series of detailed numerical experiments supports the conclusions of this analysis.
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Hakula , H & Laaksonen , M 2019 , ' Asymptotic convergence of spectral inverse iterations for stochastic eigenvalue problems ' , Numerische Mathematik , vol. 142 , no. 3 , pp. 577-609 . https://doi.org/10.1007/s00211-019-01034-w