Block and multilevel preconditioning for stochastic Galerkin problems with lognormally distributed parameters and tensor product polynomials
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F17%3A00313941" target="_blank" >RIV/68407700:21110/17:00313941 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/17:10371171
Result on the web
<a href="http://www.dl.begellhouse.com/journals/52034eb04b657aea,468587191a97aaba,3cd7c9483550940c.html" target="_blank" >http://www.dl.begellhouse.com/journals/52034eb04b657aea,468587191a97aaba,3cd7c9483550940c.html</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1615/Int.J.UncertaintyQuantification.2017020377" target="_blank" >10.1615/Int.J.UncertaintyQuantification.2017020377</a>
Alternative languages
Result language
angličtina
Original language name
Block and multilevel preconditioning for stochastic Galerkin problems with lognormally distributed parameters and tensor product polynomials
Original language description
The stochastic Galerkin method is a popular numerical method for solution of differential equations with randomly distributed data. We focus on isotropic elliptic problems with lognormally distributed coefficients. We study the block-diagonal preconditioning and the algebraic multilevel preconditioning based on the block splitting according to some hierarchy of approximation spaces for the stochastic part of the solution. We introduce upper bounds for the resulting condition numbers, and we derive a tool for obtaining sharp guaranteed upper bounds for the strengthened Cauchy-Bunyakowsky-Schwarz constant, which can serve as an indicator of the efficiency of some of these preconditioning methods. The presented multilevel approach yields a tool for efficient guaranteed two-sided a~posteriori estimates of algebraic errors and for adaptive algorithms as well.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal for Uncertainty Quantification
ISSN
2152-5080
e-ISSN
2152-5099
Volume of the periodical
7
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
22
Pages from-to
441-462
UT code for WoS article
000415634100004
EID of the result in the Scopus database
2-s2.0-85035085928