Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Accurate solutions to the square thermally driven cavity at high Rayleigh number
Computers and Fluids
Ten lectures on wavelets
Essential wavelets for statistical applications and data analysis
Essential wavelets for statistical applications and data analysis
A stochastic projection method for fluid flow. I: basic formulation
Journal of Computational Physics
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
A stochastic projection method for fluid flow II.: random process
Journal of Computational Physics
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
An Equation-Free, Multiscale Approach to Uncertainty Quantification
Computing in Science and Engineering
Beyond Wiener---Askey Expansions: Handling Arbitrary PDFs
Journal of Scientific Computing
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Uncertainty quantification of limit-cycle oscillations
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Stochastic spectral methods for efficient Bayesian solution of inverse problems
Journal of Computational Physics
Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network
Journal of Computational Physics
Generalized spectral decomposition for stochastic nonlinear problems
Journal of Computational Physics
Efficient stochastic Galerkin methods for random diffusion equations
Journal of Computational Physics
Discontinuity detection in multivariate space for stochastic simulations
Journal of Computational Physics
Uncertainty quantification for systems of conservation laws
Journal of Computational Physics
Journal of Computational Physics
Efficient uncertainty quantification with the polynomial chaos method for stiff systems
Mathematics and Computers in Simulation
A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
Journal of Computational Physics
Evolution of Probability Distribution in Time for Solutions of Hyperbolic Equations
Journal of Scientific Computing
Journal of Computational Physics
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
Numerical approach for quantification of epistemic uncertainty
Journal of Computational Physics
Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows
Journal of Computational Physics
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
Journal of Computational Physics
Adaptive sparse polynomial chaos expansion based on least angle regression
Journal of Computational Physics
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids
Journal of Computational Physics
Uncertainty investigations in nonlinear aeroelastic systems
Journal of Computational and Applied Mathematics
A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions
SIAM Journal on Scientific Computing
Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection
Journal of Scientific Computing
Journal of Computational Physics
SIAM Journal on Scientific Computing
A Posteriori Error Analysis of Parameterized Linear Systems Using Spectral Methods
SIAM Journal on Matrix Analysis and Applications
Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients
SIAM Journal on Numerical Analysis
Error analysis of generalized polynomial chaos for nonlinear random ordinary differential equations
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
Extended stochastic FEM for diffusion problems with uncertain material interfaces
Computational Mechanics
A one-time truncate and encode multiresolution stochastic framework
Journal of Computational Physics
A stochastic Galerkin method for the Euler equations with Roe variable transformation
Journal of Computational Physics
Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis
Journal of Computational Physics
Hi-index | 31.56 |
An uncertainty quantification scheme is constructed based on generalized Polynomial Chaos (PC) representations. Two such representations are considered, based on the orthogonal projection of uncertain data and solution variables using either a Haar or a Legendre basis. Governing equations for the unknown coefficients in the resulting representations are derived using a Galerkin procedure and then integrated in order to determine the behavior of the stochastic process. The schemes are applied to a model problem involving a simplified dynamical system and to the classical problem of Rayleigh-Bénard instability. For situations involving random parameters close to a critical point, the computational implementations show that the Wiener-Haar (WHa) representation provides more robust predictions that those based on a Wiener-Legendre (WLe) decomposition. However, when the solution depends smoothly on the random data, the WLe scheme exhibits superior convergence. Suggestions regarding future extensions are finally drawn based on these experiences.