Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Computational investigations of low-discrepancy sequences
ACM Transactions on Mathematical Software (TOMS)
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
Different modes of Rayleigh-Bénard instability in two- and three-dimensional rectangular enclosures
Journal of Computational Physics
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
Natural Convection in a Closed Cavity under Stochastic Non-Boussinesq Conditions
SIAM Journal on Scientific Computing
Why Are High-Dimensional Finance Problems Often of Low Effective Dimension?
SIAM Journal on Scientific Computing
Numerical Methods for Differential Equations in Random Domains
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
Journal of Computational Physics
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
Journal of Computational Physics
Error Estimates for the ANOVA Method with Polynomial Chaos Interpolation: Tensor Product Functions
SIAM Journal on Scientific Computing
A method for solving stochastic equations by reduced order models and local approximations
Journal of Computational Physics
Error Estimates for the ANOVA Method with Polynomial Chaos Interpolation: Tensor Product Functions
SIAM Journal on Scientific Computing
A probabilistic graphical model approach to stochastic multiscale partial differential equations
Journal of Computational Physics
An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling
Journal of Computational Physics
Hi-index | 31.46 |
Realistic representation of stochastic inputs associated with various sources of uncertainty in the simulation of fluid flows leads to high dimensional representations that are computationally prohibitive. We investigate the use of adaptive ANOVA decomposition as an effective dimension-reduction technique in modeling steady incompressible and compressible flows with nominal dimension of random space up to 100. We present three different adaptivity criteria and compare the adaptive ANOVA method against sparse grid, Monte Carlo and quasi-Monte Carlo methods to evaluate its relative efficiency and accuracy. For the incompressible flow problem, the effect of random temperature boundary conditions (modeled as high-dimensional stochastic processes) on the Nusselt number is investigated for different values of correlation length. For the compressible flow, the effects of random geometric perturbations (simulating random roughness) on the scattering of a strong shock wave is investigated both analytically and numerically. A probabilistic collocation method is combined with adaptive ANOVA to obtain both incompressible and compressible flow solutions. We demonstrate that for both cases even draconian truncations of the ANOVA expansion lead to accurate solutions with a speed-up factor of three orders of magnitude compared to Monte Carlo and at least one order of magnitude compared to sparse grids for comparable accuracy.