The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
Hierarchical parallelisation for the solution of stochastic finite element equations
Computers and Structures
A reduced-order random matrix approach for stochastic structural dynamics
Computers and Structures
Efficient solution for Galerkin-based polynomial chaos expansion systems
Advances in Engineering Software
Adaptive sparse polynomial chaos expansion based on least angle regression
Journal of Computational Physics
Chaos-Galerkin solution of stochastic Timoshenko bending problems
Computers and Structures
Efficient stochastic structural analysis using Guyan reduction
Advances in Engineering Software
| Hi-index | 0.00 |
We consider the situation where an unknown n-dimensional vector X has to be determined by solving a system of equations having the form F(X,v)=0, where F is a mapping from the n-dimensional Euclidean space on itself and v is a random k-dimensional vector. We focus on the numerical determination of the distribution of solution X, which is also a random variable. We propose an expansion of X as a function of a vector v and we apply known approaches such as the collocation, moment matching and variational approximation and, we developed a new approach for the solution based on the adaptation of deterministic iterative numerical methods. These approaches are tested and compared in linear and non-linear situations including a laminated composite plate and a beam under nonlinear behavior. The results showed the effectiveness and the advantages of the new approach over the variational one to solve the uncertainty quantification of systems of nonlinear equations. Also, from the comparison among the methods, it is shown that the collocation is the most effective and robust approach, followed by the adaptation one. Finally, the least robust method is the moment matching approach due to the complexity of the resulting optimization problem.