An efficient forward propagation of multiple random fields using a stochastic Galerkin scaled boundary finite element method

Abstract

This paper serves to extend the existing literature on the Stochastic Galerkin Scaled Boundary Finite Element Method (SGSBFEM) in two ways. The first part of this work deals with the formulation of multiple non-correlated Gaussian random fields using the conventional Karhunen–Loéve expansion technique and its forward propagation through the Spectral Stochastic Scaled Boundary Finite Element setting using the polynomial surface fit method in terms of the scaled boundary coordinates. The advantages in adopting such a forward propagation technique in capturing the statistical moments of Quantities of Interest (QoI) across the domain, are highlighted using carefully chosen linear elastic problems having large to least correlated random fields as inputs. The second contribution is the extension of the proposed forward Uncertainty Quantification (UQ) to take into account multiple independent random fields, followed by Polynomial Chaos Expansion (PCE) based sensitivity analysis. Both the computational efficiency and the accuracy of the proposed framework under different input random field correlation settings are elaborated upon by comparing their results against that obtained using the current existing SGSBFEM in the literature. Moreover, the stochastic results are validated for all the numerical examples using the Monte Carlo method.