Efficient calculation of uncertainty quantification

E.J.W. Maten, ter, R. Pulch, W.H.A. Schilders, H.H.J.M. Janssen

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

We consider Uncertainty Quantification (UQ) by expanding the solution in so-called generalized Polynomial Chaos expansions. In these expansions the solution is decomposed into a series with orthogonal polynomials in which the parameter dependency becomes an argument of the orthogonal polynomial basis functions. The time and space dependency remains in the coefficients. In UQ two main approaches are in use: Stochastic Collocation (SC) and Stochastic Galerkin (SG). Practice shows that in many cases SC is more efficient for similar accuracy as obtained by SG. In SC the coefficients in the expansion are approximated by quadrature and thus lead to a large series of deterministic simulations for several parameters. We consider strategies to efficiently perform this sequence of deterministic simulations within SC.
Original languageEnglish
Title of host publicationProgress in Industrial Mathematics at ECMI 2012
EditorsM. Fontes, M. Günther, N. Marheineke
Place of PublicationCham
PublisherSpringer
Pages361-370
ISBN (Print)978-3-319-05364-6
DOIs
Publication statusPublished - 2014
Event17th European Conference on Mathematics for Industry (ECMI 2012), July 23-27, 2012, Lund, Sweden - Lund, Sweden
Duration: 23 Jul 201227 Jul 2012
http://www.maths.lth.se/ecmi/ecmi2012_org/

Publication series

NameMathematics in Industry
Volume19
ISSN (Print)1612-3956

Conference

Conference17th European Conference on Mathematics for Industry (ECMI 2012), July 23-27, 2012, Lund, Sweden
Abbreviated titleECMI 2012
CountrySweden
CityLund
Period23/07/1227/07/12
Internet address

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    Maten, ter, E. J. W., Pulch, R., Schilders, W. H. A., & Janssen, H. H. J. M. (2014). Efficient calculation of uncertainty quantification. In M. Fontes, M. Günther, & N. Marheineke (Eds.), Progress in Industrial Mathematics at ECMI 2012 (pp. 361-370). (Mathematics in Industry; Vol. 19). Springer. https://doi.org/10.1007/978-3-319-05365-3_50