Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation

Authors:
M. Jardak;C.-H. Su;G. E. Karniadakis
Affiliations:
Applied Mathematics Division, Brown University, Providence, Rhode Island 02912-F;Applied Mathematics Division, Brown University, Providence, Rhode Island 02912-F;Applied Mathematics Division, Brown University, Providence, Rhode Island 02912-F. gk@cfm.brown.edu
Venue:
Journal of Scientific Computing
Year:
2002

Citing 5
Cited 10

Probabilistic finite elements for nonlinear structural dynamics

Computer Methods in Applied Mechanics and Engineering
Random media

Random media
Stochastic finite elements: a spectral approach

Stochastic finite elements: a spectral approach
The Hermite spectral method for Gaussian-type functions

SIAM Journal on Scientific Computing
Modeling uncertainty in flow simulations via generalized polynomial chaos

Journal of Computational Physics

Stochastic analysis of interconnect performance in the presence of process variations

Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics

Journal of Computational Physics
A stochastic variational multiscale method for diffusion in heterogeneous random media

Journal of Computational Physics
Sparse grid collocation schemes for stochastic natural convection problems

Journal of Computational Physics
A seamless approach towards stochastic modeling: Sparse grid collocation and data driven input models

Finite Elements in Analysis and Design
A finite element approximation of linear stochastic PDEs driven by multiplicative white noise

International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
A stochastic multiscale framework for modeling flow through random heterogeneous porous media

Journal of Computational Physics
Multi-element probabilistic collocation method in high dimensions

Journal of Computational Physics
Iterative Solvers for the Stochastic Finite Element Method

SIAM Journal on Scientific Computing
Original articles: On the linear advection equation subject to random velocity fields

Mathematics and Computers in Simulation

Quantified Score

Hi-index	0.02

Visualization

Abstract

We present a new algorithm based on Wiener–Hermite functionals combined with Fourier collocation to solve the advection equation with stochastic transport velocity. We develop different stategies of representing the stochastic input, and demonstrate that this approach is orders of magnitude more efficient than Monte Carlo simulations for comparable accuracy.