Uncertain eigenvalue analysis by the sparse grid stochastic collocation method

Abstract

In this paper, the eigenvalue problem with multiple uncertain parameters is analyzed by the sparse grid stochastic collocation method. This method provides an interpolation approach to approximate eigenvalues and eigenvectors’ functional dependencies on uncertain parameters. This method repetitively evaluates the deterministic solutions at the pre-selected nodal set to construct a high-dimensional interpolation formula of the result. Taking advantage of the smoothness of the solution in the uncertain space, the sparse grid collocation method can achieve a high order accuracy with a small nodal set. Compared with other sampling based methods, this method converges fast with the increase of the number of points. Some numerical examples with different dimensions are presented to demonstrate the accuracy and efficiency of the sparse grid stochastic collocation method.