Numerical simulation of random fields with a high-order polynomial based Ritz–Galerkin approach. (January 2019)

• Record Type: Journal Article
• Authors: Zhang, Xufang; Liu, Qian; Huang, He
• Is Part Of: Probabilistic engineering mechanics. Volume 55(2019)
• Page Start: 17
• Page End: 27
• Publication Date: 2019-01
• Subjects: Orthogonal polynomials -- Ritz–Galerkin method -- The Karhunen–Loève expansion -- Random field -- Numerical simulation; Engineering -- Statistical methods -- Periodicals; Mechanics, Applied -- Statistical methods -- Periodicals; Probabilities -- Periodicals; Ingénierie -- Méthodes statistiques -- Périodiques; Mécanique appliquée -- Méthodes statistiques -- Périodiques; Probabilités -- Périodiques; 620.100727
• DOI: 10.1016/j.probengmech.2018.08.003
• Languages: English
• ISSNs: 0266-8920

Abstract

Abstract: 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–Loève (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.