Uncertain eigenvalue analysis by the sparse grid stochastic collocation method  

作　　者：J.C.Lan X.J.Dong Z.K.Peng W.M.Zhang G.Meng 

机构地区：[1]State Key Laboratory of Mechanical Systems and Vibration,School of Mechanical Engineering, Shanghai Jiao Tong University

出　　处：《Acta Mechanica Sinica》2015年第4期545-557,共13页力学学报（英文版）

基　　金：supported by the National Nature Science Foundation of China for Distinguished Young Scholars(Grant11125209);the National Nature Science Foundation of China(Grants11322215,51121063);the Scientifi Research Foundation for the Returned Overseas Chinese Scholars

摘　　要：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 parame- ters. 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 uncer- tain 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 demon- strate the accuracy and efficiency of the sparse grid stochastic collocation method.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 parame- ters. 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 uncer- tain 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 demon- strate the accuracy and efficiency of the sparse grid stochastic collocation method.

关 键 词：Uncertainty quantification EIGENVALUE EIGENVECTOR Sparse grid Stochastic collocation methodEigenvector pairing 

分 类 号：O241.6[理学—计算数学]