Treffer: Numerical challenges in the use of polynomial chaos representations for stochastic processes

Title:
Numerical challenges in the use of polynomial chaos representations for stochastic processes
Authors:
DEBUSSCHERE, Bert J, NAJM, Habib N, PEBAY, Philippe P, KNIO, Omar M, GHANEM, Roger G, LE MAITRE, Olivier P
Source:
Special Issue on Uncertainty QuantificationSIAM journal on scientific computing (Print). 26(2):698-719
Publisher Information:
Philadelphia, PA: Society for Industrial and Applied Mathematics, 2005.
Publication Year:
2005
Physical Description:
print, 31 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Fonctions spéciales, Special functions, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Probabilités et statistiques, Probability and statistics, Théorie des probabilités et processus stochastiques, Probability theory and stochastic processes, Processus stochastiques, Stochastic processes, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Probabilités et statistiques numériques, Numerical methods in probability and statistics, Analyse numérique, Numerical analysis, Análisis numérico, Calcul scientifique, Scientific computation, Computación científica, Evaluation fonction, Function evaluation, Intégration, Integration, Integración, Méthode projection, Projection method, Método proyección, Méthode spectrale, Spectral method, Método espectral, Processus stochastique, Stochastic process, Proceso estocástico, Relation incertitude, Uncertainty relation, Relación incertitud, Simulation numérique, Numerical simulation, Simulación numérica, Série Taylor, Taylor series, Serie Taylor, 28XX, 60G05, 60G99, Chaos polynomial, Polynomial chaos, 33C45, 37H10, 65C20, polynomial chaos, spectral uncertainty quantification 60G99, stochastic
Document Type:
Konferenz Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Sandia National Labs, 7011 East Ave., MS 9051, Livermore, CA 94550, United States
The Johns Hopkins University, Baltimore, MD 21218, United States
Université d'Evry Val d'Essonne, Evry, France
ISSN:
1064-8275
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=16610812
Rights:
Copyright 2005 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.16610812
Database:
PASCAL Archive

Weitere Informationen

This paper gives an overview of the use of polynomial chaos (PC) expansions to represent stochastic processes in numerical simulations. Several methods are presented for performing arithmetic on, as well as for evaluating polynomial and nonpolynomial functions of variables represented by PC expansions. These methods include Taylor series, a newly developed integration method, as well as a sampling-based spectral projection method for nonpolynomial function evaluations. A detailed analysis of the accuracy of the PC representations, and of the different methods for nonpolynomial function evaluations, is performed. It is found that the integration method offers a robust and accurate approach for evaluating nonpolynomial functions, even when very high-order information is present in the PC expansions.