An efficient reduced-order method for stochastic eigenvalue analysis

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.