Efficient characterization of the random eigenvalue problem in a polynomial chaos decomposition

2007 ◽  
Vol 72 (4) ◽  
pp. 486-504 ◽  
Author(s):  
Roger Ghanem ◽  
Debraj Ghosh
Keyword(s):  
Eigenvalue Problem ◽  
Polynomial Chaos ◽  
Chaos Decomposition ◽  
Random Eigenvalue ◽  
Random Eigenvalue Problem

An Enrichment Scheme for Polynomial Chaos Expansion Applied to Random Eigenvalue Problem

2005 ◽  
Author(s):  
Roger Ghanem ◽  
Debraj Ghosh
Keyword(s):  
Eigenvalue Problem ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Eigenvalues And Eigenvectors ◽  
System Parameters ◽  
Statistical Behavior ◽  
Random Eigenvalue ◽  
Clustered Eigenvalues ◽  
Random Eigenvalue Problem

For a system with the parameters modeled as uncertain, polynomial approximations such as polynomial chaos expansion provide an effective way to estimate the statistical behavior of the eigenvalues and eigenvectors, provided the eigenvalues are widely spaced. For a system with a set of clustered eigenvalues, the corresponding eigenvalues and eigenvectors are very sensitive to perturbation of the system parameters. An enrichment scheme to the polynomial chaos expansion is proposed here in order to capture the behavior of such eigenvalues and eigenvectors. It is observed that for judiciously chosen enrichment functions, the enriched expansion provides better estimate of the statistical behavior of the eigenvalues and eigenvectors.

Spectral Power Iterations for the Random Eigenvalue Problem

AIAA Journal ◽  
2014 ◽  
Vol 52 (5) ◽  
pp. 912-925 ◽  
Author(s):  
Hadi Meidani ◽  
Roger Ghanem
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Power ◽  
Random Eigenvalue ◽  
Random Eigenvalue Problem

Homotopy approach for random eigenvalue problem

2017 ◽  
Vol 113 (3) ◽  
pp. 450-478 ◽  
Author(s):  
Bin Huang ◽  
Heng Zhang ◽  
Kok-Kwang Phoon
Keyword(s):  
Eigenvalue Problem ◽  
Random Eigenvalue ◽  
Random Eigenvalue Problem
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