Efficient and portable combined random number generators
Communications of the ACM
Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Monomial cubature rules since “Stroud”: a compilation—part 2
Journal of Computational and Applied Mathematics - Numerical evaluation of integrals
Quadrature formulas for the Wiener measure
Journal of Complexity
Advances in Engineering Software - Special issue on large-scale analysis, design and intelligent synthesis environments
Journal of Computational Physics
Higher-Dimensional Integration with Gaussian Weight for Applications in Probabilistic Design
SIAM Journal on Scientific Computing
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
SIAM Journal on Scientific Computing
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
A stochastic variational multiscale method for diffusion in heterogeneous random media
Journal of Computational Physics
Hermite expansions in Monte-Carlo computation
Journal of Computational Physics
SIAM Journal on Scientific Computing
Bayesian inference with optimal maps
Journal of Computational Physics
Hi-index | 31.45 |
We examine a variety of polynomial-chaos-motivated approximations to a stochastic form of a steady state groundwater flow model. We consider approaches for truncating the infinite dimensional problem and producing decoupled systems. We discuss conditions under which such decoupling is possible and show that to generalize the known decoupling by numerical cubature, it would be necessary to find new multivariate cubature rules. Finally, we use the acceleration of Monte Carlo to compare the quality of polynomial models obtained for all approaches and find that in general the methods considered are more efficient than Monte Carlo for the relatively small domains considered in this work. A curse of dimensionality in the series expansion of the log-normal stochastic random field used to represent hydraulic conductivity provides a significant impediment to efficient approximations for large domains for all methods considered in this work, other than the Monte Carlo method.