Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: A numerical comparison

Handle URI:
http://hdl.handle.net/10754/575778
Title:
Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: A numerical comparison
Authors:
Bäck, Joakim; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
Much attention has recently been devoted to the development of Stochastic Galerkin (SG) and Stochastic Collocation (SC) methods for uncertainty quantification. An open and relevant research topic is the comparison of these two methods. By introducing a suitable generalization of the classical sparse grid SC method, we are able to compare SG and SC on the same underlying multivariate polynomial space in terms of accuracy vs. computational work. The approximation spaces considered here include isotropic and anisotropic versions of Tensor Product (TP), Total Degree (TD), Hyperbolic Cross (HC) and Smolyak (SM) polynomials. Numerical results for linear elliptic SPDEs indicate a slight computational work advantage of isotropic SC over SG, with SC-SM and SG-TD being the best choices of approximation spaces for each method. Finally, numerical results corroborate the optimality of the theoretical estimate of anisotropy ratios introduced by the authors in a previous work for the construction of anisotropic approximation spaces. © 2011 Springer.
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Stochastic Numerics Research Group
Publisher:
Springer Science + Business Media
Journal:
Spectral and High Order Methods for Partial Differential Equations
Conference/Event name:
ICOSAHOM '09 conference
Issue Date:
17-Sep-2010
DOI:
10.1007/978-3-642-15337-2_3
Type:
Conference Paper
ISSN:
14397358
ISBN:
9783642153365
Appears in Collections:
Conference Papers; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBäck, Joakimen
dc.contributor.authorNobile, Fabioen
dc.contributor.authorTamellini, Lorenzoen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2015-08-24T09:25:57Zen
dc.date.available2015-08-24T09:25:57Zen
dc.date.issued2010-09-17en
dc.identifier.isbn9783642153365en
dc.identifier.issn14397358en
dc.identifier.doi10.1007/978-3-642-15337-2_3en
dc.identifier.urihttp://hdl.handle.net/10754/575778en
dc.description.abstractMuch attention has recently been devoted to the development of Stochastic Galerkin (SG) and Stochastic Collocation (SC) methods for uncertainty quantification. An open and relevant research topic is the comparison of these two methods. By introducing a suitable generalization of the classical sparse grid SC method, we are able to compare SG and SC on the same underlying multivariate polynomial space in terms of accuracy vs. computational work. The approximation spaces considered here include isotropic and anisotropic versions of Tensor Product (TP), Total Degree (TD), Hyperbolic Cross (HC) and Smolyak (SM) polynomials. Numerical results for linear elliptic SPDEs indicate a slight computational work advantage of isotropic SC over SG, with SC-SM and SG-TD being the best choices of approximation spaces for each method. Finally, numerical results corroborate the optimality of the theoretical estimate of anisotropy ratios introduced by the authors in a previous work for the construction of anisotropic approximation spaces. © 2011 Springer.en
dc.publisherSpringer Science + Business Mediaen
dc.subjectElliptic equationsen
dc.subjectMultivariate polynomial approximationen
dc.subjectPDEs with random dataen
dc.subjectSmolyak approximationen
dc.subjectStochastic collocation methodsen
dc.subjectStochastic Galerkin methodsen
dc.subjectUncertainty quantificationen
dc.titleStochastic spectral Galerkin and collocation methods for PDEs with random coefficients: A numerical comparisonen
dc.typeConference Paperen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentStochastic Numerics Research Groupen
dc.identifier.journalSpectral and High Order Methods for Partial Differential Equationsen
dc.conference.dateJune 22-26 2009en
dc.conference.nameICOSAHOM '09 conferenceen
dc.conference.locationTrondheim, Norwayen
dc.contributor.institutionMOX, Department of Mathematics F. Brioschi, Politecnico di Milano, Italyen
kaust.authorTempone, Raulen
kaust.authorBäck, Joakimen
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