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 

作者机构：State Key Laboratory of Mechanical Systems and VibrationSchool of Mechanical Engineering Shanghai Jiao Tong University 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2015年第31卷第4期

页      面：545-557页

核心收录：

学科分类：07[理学] 0802[工学-机械工程] 070102[理学-计算数学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学] 

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 

主　　题：Uncertainty quantification Eigenvalue Eigenvector Sparse grid Stochastic collocation methodEigenvector pairing 

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.