Premium
An extended stochastic pseudo‐spectral Galerkin finite element method (XS‐PS‐GFEM) for elliptic equations with hybrid uncertainties
Author(s) -
Varghese Mathew Tittu,
Rebbagondla Jayamanideep,
Natarajan Sundararajan
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6433
Subject(s) - polynomial chaos , sobol sequence , finite element method , mathematics , galerkin method , random field , spectral method , uncertainty quantification , monte carlo method , spectral element method , mathematical optimization , mathematical analysis , mixed finite element method , physics , thermodynamics , statistics
Summary Nouy and Clement introduced the stochastic extended finite element method to solve linear elasticity problem defined on random domain. The material properties and boundary conditions were assumed to be deterministic. In this work, we extend this framework to account for multiple independent input uncertainties, namely, material, geometry, and external force uncertainties. The stochastic field is represented using the polynomial chaos expansion. The challenge in numerical integration over multidimensional probabilistic space is addressed using the pseudo‐spectral Galerkin method. Thereafter, a sensitivity analysis based on Sobol indices using the derived stochastic extended Finite Element Method solution is presented. The efficiency and accuracy of the proposed novel framework against conventional Monte Carlo methods is elucidated in detail for a few one and two dimensional problems.