Numerical simulation of random fields with a high-order polynomial based Ritz-Galerkin approach

作者：Zhang, Xufang^*; Liu, Qian; Huang, He

来源：Probabilistic Engineering Mechanics, 2019, 55: 17-27.

DOI：10.1016/j.probengmech.2018.08.003

• Orthogonal polynomials
• Ritz-Galerkin method
• The Karhunen-Lotve expansion
• Random field
• Numerical simulation

The uncertainty simulation related to a spatially varying physical property requires the theory of the random field discretization. A random field in definition consists of an infinite number of random variables that are attached to all points within the simulation domain. The utility of the Karhunen-Loeve (K-L) expansion allows representing a second-order random field as the summation of a few deterministic functions and standard random variables. However, the K-L expansion depends on exact eigensolutions of the Fredholm integral equation of the second kind. Along with an emerging trend of the random field simulation combined with a complex geometry, analytical expansion results are increasingly inapplicable in engineering reality. To this end, the paper presents a high-order polynomial based Ritz-Galerkin approach. To implement, the Legendre, the Chebyshev, and the Gegenbauer orthogonal polynomials are used to realize the Ritz-Galerkin approximation. Together with the Gaussian-quadrature based interpolation scheme in approximating covariance models, numerical results for eigensolutions have demonstrated the spectral accuracy of the proposed approach. Results for the non-stationary, non-Gaussian and multivariate random field simulations have validated the high-order polynomial based Ritz-Galerkin approach has engineering applications.

• 出版日期2019-1
• 单位东北大学