Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Spanning the length scales in dynamic simulation
Computers in Physics
On an interpolatory method for high dimensional integration
Journal of Computational and Applied Mathematics - Numerical evaluation of integrals
Understanding Molecular Simulation: From Algorithms to Applications
Understanding Molecular Simulation: From Algorithms to Applications
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation
Journal of Scientific Computing
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation
SIAM Journal on Scientific Computing
Using stochastic analysis to capture unstable equilibrium in natural convection
Journal of Computational Physics
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
Algorithm 847: Spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Stochastic analysis of transport in tubes with rough walls
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Performance evaluation of generalized polynomial chaos
ICCS'03 Proceedings of the 2003 international conference on Computational science
Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network
Journal of Computational Physics
Inversion of Robin coefficient by a spectral stochastic finite element approach
Journal of Computational Physics
Finite Elements in Analysis and Design
Journal of Computational Physics
A non-linear dimension reduction methodology for generating data-driven stochastic input models
Journal of Computational Physics
Journal of Computational Physics
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
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
A stochastic multiscale framework for modeling flow through random heterogeneous porous media
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
A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
Journal of Computational Physics
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
Journal of Computational Physics
Numerical approach for quantification of epistemic uncertainty
Journal of Computational Physics
Journal of Computational Physics
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
Journal of Computational Physics
Journal of Computational Physics
WSEAS TRANSACTIONS on SYSTEMS
Adaptive sparse polynomial chaos expansion based on least angle regression
Journal of Computational Physics
A stochastic mixed finite element heterogeneous multiscale method for flow in porous media
Journal of Computational Physics
Kernel principal component analysis for stochastic input model generation
Journal of Computational Physics
Adaptive ANOVA decomposition of stochastic incompressible and compressible flows
Journal of Computational Physics
Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection
Journal of Scientific Computing
A method for solving stochastic equations by reduced order models and local approximations
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
A Sparse Composite Collocation Finite Element Method for Elliptic SPDEs.
SIAM Journal on Numerical Analysis
An adaptive dimension decomposition and reselection method for reliability analysis
Structural and Multidisciplinary Optimization
A one-time truncate and encode multiresolution stochastic framework
Journal of Computational Physics
Preconditioned Bayesian Regression for Stochastic Chemical Kinetics
Journal of Scientific Computing
Computers & Mathematics with Applications
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In recent years, there has been an interest in analyzing and quantifying the effects of random inputs in the solution of partial differential equations that describe thermal and fluid flow problems. Spectral stochastic methods and Monte-Carlo based sampling methods are two approaches that have been used to analyze these problems. As the complexity of the problem or the number of random variables involved in describing the input uncertainties increases, these approaches become highly impractical from implementation and convergence points-of-view. This is especially true in the context of realistic thermal flow problems, where uncertainties in the topology of the boundary domain, boundary flux conditions and heterogeneous physical properties usually require high-dimensional random descriptors. The sparse grid collocation method based on the Smolyak algorithm offers a viable alternate method for solving high-dimensional stochastic partial differential equations. An extension of the collocation approach to include adaptive refinement in important stochastic dimensions is utilized to further reduce the numerical effort necessary for simulation. We show case the collocation based approach to efficiently solve natural convection problems involving large stochastic dimensions. Equilibrium jumps occurring due to surface roughness and heterogeneous porosity are captured. Comparison of the present method with the generalized polynomial chaos expansion and Monte-Carlo methods are made.