Time-dependent generalized polynomial chaos

Gerritsma, Marc; Steen, Jan‐Bart van der; Vos, Peter; Karniadakis, George

doi:10.1016/j.jcp.2010.07.020

Cited by 162 publications

(150 citation statements)

References 32 publications

Supporting

Mentioning

149

Contrasting

Order By: Relevance

“…Another approach to addressing the long-term simulation accuracy of gPC was developed by Gerritsma and coworkers [35]; their approach constructs a new set of orthogonal polynomials adaptively as the probability density function (PDF) evolves with time. Their work has shown that the adaptively contrustructed polynomial basis allows for lower order approximations that have improved convergence for long-term simulations.…”

Section: 24mentioning

confidence: 99%

Parametric Design Optimization of Uncertain Ordinary Differential Equation Systems

Hays

Sandu

et al. 2011

Volume 9: Transportation Systems; Safety Engineering, Risk Analysis and Reliability Methods; Applied Stochastic Optimization, U

View full text Add to dashboard Cite

show abstract

Section: 24mentioning

confidence: 99%

Parametric Design Optimization of Uncertain Ordinary Differential Equation Systems

Hays

Sandu

et al. 2011

Volume 9: Transportation Systems; Safety Engineering, Risk Analysis and Reliability Methods; Applied Stochastic Optimization, U

View full text Add to dashboard Cite

show abstract

“…However, in practice, optimal convergence is limited to stochastic processes with Gaussian inputs ξ i . Otherwise, numerical results deteriorate even for early times [11].…”

Section: Introductionmentioning

confidence: 97%

Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach

Chen-Charpentier

López

Licea

et al. 2015

Mathematics and Computers in Simulation

View full text Add to dashboard Cite

ElsevierChen Charpentier, BM.; Cortés, J.; Licea Salazar, JA.; Romero, J.; Roselló Ferragud, MD.; Santonja, F.; Villanueva Micó, RJ. (2015). Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach. AbstractDue to errors in measurements and inherent variability in the quantities of interest, models based on random differential equations give more realistic results than their deterministic counterpart. The generalized polynomial chaos (gPC) is a powerful technique used to approximate the solution of these equations when the random inputs follow standard probability distributions. But in many cases these random inputs do not have a standard probability distribution. In this paper, we present a step-by-step constructive methodology to implement directly a useful version of adaptive gPC for arbitrary distributions, extending the applicability of the gPC. The paper mainly focuses on the computational aspects, on the implementation of the method and on the creation of a useful software tool. This tool allows the user to easily change the types of distributions and the order of the expansions, and to study their the usefulness of the method are included.

show abstract

“…[24], then the three triple integrals and joint probability density functions in Eqs. (49)~(51) can be transformed into…”

mentioning

confidence: 99%

Correction: Uncertainty Quantification for Mars Atmospheric Entry using Polynomial Chaos and Spectral Decomposition

Jiang

2018

2018 AIAA Guidance, Navigation, and Control Conference

View full text Add to dashboard Cite

Abstract, "… and other system parameters." is revised to be "… and model parameters." 2. The second sentence of the Abstract, "The framework is built on the generalized polynomial chaos expansions and spectral decomposition." is revised to be "The framework is built via generalized polynomial chaos expansions and spectral decomposition."3. The last sentence of the Abstract, "…, in mars entry dynamics profile, with the same order of accuracy as the Monte-Carlo methods but with more computational efficiency." is revised to be "…, in Mars entry dynamics profile, with higher computational efficiency than Monte-Carlo technique and higher accuracy than generalized polynomial chaos.".4. At the beginning of the second sentence in the second paragraph of section I, "It enabling the assessment …" is revised to be "It enables the assessment …".

show abstract

Time-dependent generalized polynomial chaos

Cited by 162 publications

References 32 publications

Parametric Design Optimization of Uncertain Ordinary Differential Equation Systems

Parametric Design Optimization of Uncertain Ordinary Differential Equation Systems

Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach

Correction: Uncertainty Quantification for Mars Atmospheric Entry using Polynomial Chaos and Spectral Decomposition

Contact Info

Product

Resources

About