Stochastic analysis of transport in tubes with rough walls
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Stochastic Computational Fluid Mechanics
Computing in Science and Engineering
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network
Journal of Computational Physics
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
Stochastic integral equation solver for efficient variation-aware interconnect extraction
Proceedings of the 45th annual Design Automation Conference
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
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
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
Journal of Computational Physics
Discontinuity detection in multivariate space for stochastic simulations
Journal of Computational Physics
A capacitance solver for incremental variation-aware extraction
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Journal of Computational Physics
Spectral approximation of solutions to the chemical master equation
Journal of Computational and Applied Mathematics
A least-squares approximation of partial differential equations with high-dimensional random inputs
Journal of Computational Physics
A generalized polynomial chaos based ensemble Kalman filter with high accuracy
Journal of Computational Physics
Polynomial chaos for multirate partial differential algebraic equations with random parameters
Applied Numerical Mathematics
Padé-Legendre approximants for uncertainty analysis with discontinuous response surfaces
Journal of Computational Physics
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
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
Binning optimization based on SSTA for transparently-latched circuits
Proceedings of the 2009 International Conference on Computer-Aided Design
Journal of Computational Physics
Numerical approach for quantification of epistemic uncertainty
Journal of Computational Physics
Journal of Computational Physics
A high order multivariate approximation scheme for scattered data sets
Journal of Computational Physics
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
Journal of Computational Physics
Stochastic dominant singular vectors method for variation-aware extraction
Proceedings of the 47th Design Automation Conference
Journal of Computational Physics
Hybrid energy storage system integration for vehicles
Proceedings of the 16th ACM/IEEE international symposium on Low power electronics and design
Evaluation of failure probability via surrogate models
Journal of Computational Physics
Variation-aware interconnect extraction using statistical moment preserving model order reduction
Proceedings of the Conference on Design, Automation and Test in Europe
Adaptive sparse grid algorithms with applications to electromagnetic scattering under uncertainty
Applied Numerical Mathematics
Ambrosio-tortorelli segmentation of stochastic images
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Adaptive sparse polynomial chaos expansion based on least angle regression
Journal of Computational Physics
Modelling and simulation of autonomous oscillators with random parameters
Mathematics and Computers in Simulation
A non-adapted sparse approximation of PDEs with stochastic inputs
Journal of Computational Physics
Sparse Tensor Discretization of Elliptic sPDEs
SIAM Journal on Scientific Computing
Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids
Journal of Computational Physics
Efficient stochastic structural analysis using Guyan reduction
Advances in Engineering Software
A stochastic mixed finite element heterogeneous multiscale method for flow in porous media
Journal of Computational Physics
Uncertainty investigations in nonlinear aeroelastic systems
Journal of Computational and Applied Mathematics
Kernel principal component analysis for stochastic input model generation
Journal of Computational Physics
Stochastic based sensitivity function for model level selection in system simulation
Proceedings of the 2010 Conference on Grand Challenges in Modeling & Simulation
Spectral Methods for Parameterized Matrix Equations
SIAM Journal on Matrix Analysis and Applications
A Stochastic Mortar Mixed Finite Element Method for Flow in Porous Media with Multiple Rock Types
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection
Journal of Scientific Computing
Journal of Computational Physics
Generalised Polynomial Chaos for a Class of Linear Conservation Laws
Journal of Scientific Computing
Multi-output local Gaussian process regression: Applications to uncertainty quantification
Journal of Computational Physics
A method for solving stochastic equations by reduced order models and local approximations
Journal of Computational Physics
Probability density evolution analysis of engineering structures via cubature points
Computational Mechanics
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
A Sparse Composite Collocation Finite Element Method for Elliptic SPDEs.
SIAM Journal on Numerical Analysis
Polynomial chaos for boundary value problems of dynamical systems
Applied Numerical Mathematics
Wave scattering by randomly shaped objects
Applied Numerical Mathematics
Structural and Multidisciplinary Optimization
Journal of Computational Physics
An upscaling method using coefficient splitting and its applications to elliptic PDEs
Computers & Mathematics with Applications
Simplex stochastic collocation with ENO-type stencil selection for robust uncertainty quantification
Journal of Computational Physics
Robust topology optimization accounting for misplacement of material
Structural and Multidisciplinary Optimization
An adaptive dimension decomposition and reselection method for reliability analysis
Structural and Multidisciplinary Optimization
A flexible numerical approach for quantification of epistemic uncertainty
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A probabilistic graphical model approach to stochastic multiscale partial differential equations
Journal of Computational Physics
Extended stochastic FEM for diffusion problems with uncertain material interfaces
Computational Mechanics
Subcell resolution in simplex stochastic collocation for spatial discontinuities
Journal of Computational Physics
Uncertainty quantification for algebraic systems of equations
Computers and Structures
Uncertainty quantification for integrated circuits: stochastic spectral methods
Proceedings of the International Conference on Computer-Aided Design
Journal of Computational Physics
An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling
Journal of Computational Physics
Adaptive approximation of higher order posterior statistics
Journal of Computational Physics
Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
High-order methods as an alternative to using sparse tensor products for stochastic Galerkin FEM
Computers & Mathematics with Applications
Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems
Journal of Scientific Computing
Scientific Programming - A New Overview of the Trilinos Project --Part 1
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Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling methods. However, when the governing equations take complicated forms, numerical implementations of stochastic Galerkin methods can become nontrivial and care is needed to design robust and efficient solvers for the resulting equations. On the other hand, the traditional sampling methods, e.g., Monte Carlo methods, are straightforward to implement, but they do not offer convergence as fast as stochastic Galerkin methods. In this paper, a high-order stochastic collocation approach is proposed. Similar to stochastic Galerkin methods, the collocation methods take advantage of an assumption of smoothness of the solution in random space to achieve fast convergence. However, the numerical implementation of stochastic collocation is trivial, as it requires only repetitive runs of an existing deterministic solver, similar to Monte Carlo methods. The computational cost of the collocation methods depends on the choice of the collocation points, and we present several feasible constructions. One particular choice, based on sparse grids, depends weakly on the dimensionality of the random space and is more suitable for highly accurate computations of practical applications with large dimensional random inputs. Numerical examples are presented to demonstrate the accuracy and efficiency of the stochastic collocation methods.