Computational investigations of low-discrepancy sequences
ACM Transactions on Mathematical Software (TOMS)
Foundations of Quantization for Probability Distributions
Foundations of Quantization for Probability Distributions
Generalized Green's Functions and the Effective Domain of Influence
SIAM Journal on Scientific Computing
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
SIAM Journal on Scientific Computing
Journal of Computational Physics
Karhunen-Loève approximation of random fields by generalized fast multipole methods
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
Journal of Computational Physics
Probabilistic models for stochastic elliptic partial differential equations
Journal of Computational Physics
Numerical Methods for Stochastic Computations: A Spectral Method Approach
Numerical Methods for Stochastic Computations: A Spectral Method Approach
Adaptive ANOVA decomposition of stochastic incompressible and compressible flows
Journal of Computational Physics
Hi-index | 31.45 |
A method is proposed for solving equations with random entries, referred to as stochastic equations (SEs). The method is based on two recent developments. The first approximates the response surface giving the solution of a stochastic equation as a function of its random parameters by a finite set of hyperplanes tangent to it at expansion points selected by geometrical arguments. The second approximates the vector of random parameters in the definition of a stochastic equation by a simple random vector, referred to as stochastic reduced order model (SROM), and uses it to construct a SROM for the solution of this equation. The proposed method is a direct extension of these two methods. It uses SROMs to select expansion points, rather than selecting these points by geometrical considerations, and represents the solution by linear and/or higher order local approximations. The implementation and the performance of the method are illustrated by numerical examples involving random eigenvalue problems and stochastic algebraic/differential equations. The method is conceptually simple, non-intrusive, efficient relative to classical Monte Carlo simulation, accurate, and guaranteed to converge to the exact solution.