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dc.contributor.author
Dick, Josef
dc.contributor.author
Kuo, Frances Y.
dc.contributor.author
LeGia, Quoc T.
dc.contributor.author
Schwab, Christoph
dc.date.accessioned
2018-03-09T14:40:26Z
dc.date.available
2017-06-11T14:43:35Z
dc.date.available
2018-03-09T14:40:26Z
dc.date.issued
2014-06
dc.identifier.uri
http://hdl.handle.net/20.500.11850/94625
dc.identifier.doi
10.3929/ethz-a-010386245
dc.description.abstract
We develop a convergence analysis of a multi-level algorithm combining higher order quasi-Monte Carlo (QMC) quadratures with general Petrov-Galerkin discretizations of countably affine parametric operator equations of elliptic and parabolic type, extending both the multi-Level first order analysis in [F.Y. Kuo, Ch. Schwab, and I.H. Sloan, Multi-level quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficient (in review)] and the single level higher order analysis in [J. Dick, F.Y. Kuo, Q.T. Le Gia, D. Nuyens, and Ch. Schwab, Higher order QMC Galerkin discretization for parametric operator equations (in review)]. We cover, in particular, both definite as well as indefinite, strongly elliptic systems of partial differential equations (PDEs) in non-smooth domains, and discuss in detail the impact of higher order derivatives of Karhunen-Loève eigenfunctions in the parametrization of random PDE inputs on the convergence results. Based on our a-priori error bounds, concrete choices of algorithm Parameters are proposed in order to achieve a prescribed accuracy under minimal computational work. Problem classes and sufficient conditions on data are identified where multi-level higher order QMC Petrov-Galerkin algorithms outperform the corresponding single level versions of these algorithms.
en_US
dc.language.iso
en
en_US
dc.publisher
ETH Zürich
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.subject
GALERKIN METHOD (NUMERICAL MATHEMATICS)
en_US
dc.subject
Infinite dimensional quadrature
en_US
dc.subject
STOCHASTISCHE APPROXIMATION + MONTE-CARLO-METHODEN (STOCHASTIK)
en_US
dc.subject
higher order digital nets
en_US
dc.subject
Affine parametric operator equations
en_US
dc.subject
Petrov- Galerkin discretization
en_US
dc.subject
LINEARE OPERATOREN UND OPERATORENGLEICHUNGEN (FUNKTIONALANALYSIS)
en_US
dc.subject
Multi-level methods
en_US
dc.subject
LINEAR OPERATORS AND OPERATOR EQUATIONS (FUNCTIONAL ANALYSIS)
en_US
dc.subject
QUADRATURE FORMULAS (NUMERICAL MATHEMATICS)
en_US
dc.subject
STOCHASTIC APPROXIMATION + MONTE CARLO METHODS (STOCHASTICS)
en_US
dc.subject
Quasi-Monte Carlo methods
en_US
dc.subject
Interlaced polynomial lattice rules
en_US
dc.subject
QUADRATURFORMELN (NUMERISCHE MATHEMATIK)
en_US
dc.subject
GALERKIN-VERFAHREN (NUMERISCHE MATHEMATIK)
en_US
dc.title
Multi-level higher order QMC Galerkin discretization for affine parametric operator equations
en_US
dc.type
Report
dc.rights.license
In Copyright - Non-Commercial Use Permitted
dc.date.published
2015
ethz.journal.title
Research Report
ethz.journal.volume
2014-14
en_US
ethz.journal.issue
14
en_US
ethz.size
27 p.
en_US
ethz.code.ddc
5 - Science::510 - Mathematics
en_US
ethz.grant
Automated Urban Parking and Driving
en_US
ethz.identifier.nebis
010386245
ethz.publication.place
Zürich
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
en_US
ethz.grant.agreementno
247277
ethz.grant.fundername
EC
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
FP7
ethz.date.deposited
2017-06-11T14:43:50Z
ethz.source
ECOL
ethz.source
ECIT
ethz.identifier.importid
imp593652af2e25178100
ethz.identifier.importid
imp59366b6f05cf323884
ethz.ecolpid
eth:47360
ethz.ecitpid
pub:148575
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2017-07-14T22:35:28Z
ethz.rosetta.lastUpdated
2018-11-06T15:33:09Z
ethz.rosetta.versionExported
true
ethz.COinS
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