Topic
Polynomial chaos
About: Polynomial chaos is a research topic. Over the lifetime, 3700 publications have been published within this topic receiving 86289 citations.
Papers published on a yearly basis
Papers
More filters
[...]
TL;DR: In this paper, the authors discuss the Wiener-Ito chaos decomposition of an L 2 function
Abstract: This paper discusses the Wiener-Ito chaos decomposition of an L 2 function
666 citations
Journal Article•
TL;DR: This paper presents a review of the current state-of-the-art of numerical methods for stochastic computations, with a particular emphasis on those based on generalized polynomial chaos (gPC) methodology.
Abstract: This paper presents a review of the current state-of-the-art of numerical methods for stochastic computations. The focus is on efficient high-order methods suitable for practical applications, with a particular emphasis on those based on generalized polynomial chaos (gPC) methodology. The framework of gPC is reviewed, along with its Galerkin and collocation approaches for solving stochastic equations. Properties of these methods are summarized by using results from literature. This paper also attempts to present the gPC based methods in a unified framework based on an extension of the classical spectral methods into multi-dimensional random spaces. AMS subject classifications: 41A10, 60H35, 65C30, 65C50
665 citations
TL;DR: It is shown that when the model output is smooth with regards to the inputs, a spectral convergence of the computed sensitivity indices is achieved, but even for smooth outputs the method is limited to a moderate number of inputs, as it becomes computationally too demanding to reach the convergence domain.
643 citations
Book•
28 Jun 1998TL;DR: In this article, the authors present a model of dynamical systems and their linear stability with topological chaos, Liouvillian dynamics, and Probabalistic chaos, and Scattering theory of transport.
Abstract: 1. Dynamical systems and their linear stability 2. Topological chaos 3. Liouvillian dynamics 4. Probabalistic chaos 5. Chaotic scattering 6. Scattering theory of transport 7. Hydrodynamic modes of diffusion 8. Systems maintained out of equilibrium 9. Noises as microscopic chaos.
641 citations
TL;DR: A Multi-Element generalized Polynomial Chaos (ME-gPC) method to deal with long-term integration and discontinuities in stochastic differential equations and demonstrates its effectiveness for ODEs, including the Kraichnan-Orszag three-mode problem, as well as advection-diffusion problems.
591 citations