A powerful tool in computational stochastic mechanics is the stochastic finite element
method (SFEM). SFEM is an extension of the classical deterministic FE approach to the …

Based on the Gegenbauer polynomial expansion theory and regularization method, an
analytical method is proposed to identify dynamic loads acting on stochastic structures …

A computational methodology is developed to address the solution of high-dimensional
stochastic problems. It utilizes high-dimensional model representation (HDMR) technique in …

Independent sampling of orthogonal polynomial bases via Monte Carlo is of interest for
uncertainty quantification of models using Polynomial Chaos (PC) expansions. It is known …

We consider the problem of numerically approximating the solution of an elliptic partial
differential equation with random coefficients and homogeneous Dirichlet boundary …

We formulate, and present a numerical method for solving, an inverse problem for inferring
parameters of a deterministic model from stochastic observational data on quantities of …

For the nonlinear Richards equation as an unsaturated flow through heterogeneous media,
we build a new coarse-scale approximation algorithm utilizing numerical homogenization …

We propose and analyze an efficient ensemble algorithm with artificial compressibility (AC)
for fast decoupled computation of multiple realizations of the stochastic Stokes‐Darcy model …

In this paper, we consider a coarse grid approximation (numerical homogenization and
multiscale finite element method) for the poroelasticity problem with stochastic properties …

A multigrid multilevel Monte Carlo (MGMLMC) method is developed for the stochastic Stokes–
Darcy interface model with random hydraulic conductivity both in the porous media domain …