Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
Weighted tensor product algorithms for linear multivariate problems
Journal of Complexity
Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
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
A stochastic projection method for fluid flow II.: random process
Journal of Computational Physics
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
Why Are High-Dimensional Finance Problems Often of Low Effective Dimension?
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 - 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
SIAM Journal on Numerical Analysis
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
Journal of Computational Physics
Journal of Computational Physics
Structural and Multidisciplinary Optimization
Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications
Journal of Computational Physics
Adaptive ANOVA decomposition of stochastic incompressible and compressible flows
Journal of Computational Physics
Journal of Computational Physics
Galerkin Methods for Stochastic Hyperbolic Problems Using Bi-Orthogonal Polynomials
Journal of Scientific Computing
Error Estimates for the ANOVA Method with Polynomial Chaos Interpolation: Tensor Product Functions
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
Journal of Computational Physics
An adaptive dimension decomposition and reselection method for reliability analysis
Structural and Multidisciplinary Optimization
Journal of Computational Physics
A simplex-based numerical framework for simple and efficient robust design optimization
Computational Optimization and Applications
A one-time truncate and encode multiresolution stochastic framework
Journal of Computational Physics
An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling
Journal of Computational Physics
Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis
Journal of Computational Physics
Hi-index | 31.50 |
We combine multi-element polynomial chaos with analysis of variance (ANOVA) functional decomposition to enhance the convergence rate of polynomial chaos in high dimensions and in problems with low stochastic regularity. Specifically, we employ the multi-element probabilistic collocation method MEPCM [1] and so we refer to the new method as MEPCM-A. We investigate the dependence of the convergence of MEPCM-A on two decomposition parameters, the polynomial order @m and the effective dimension @n, with @n@?N, and N the nominal dimension. Numerical tests for multi-dimensional integration and for stochastic elliptic problems suggest that @n=@m for monotonic convergence of the method. We also employ MEPCM-A to obtain error bars for the piezometric head at the Hanford nuclear waste site under stochastic hydraulic conductivity conditions. Finally, we compare the cost of MEPCM-A against Monte Carlo in several hundred dimensions, and we find MEPCM-A to be more efficient for up to 600 dimensions for a specific multi-dimensional integration problem involving a discontinuous function.