Hierarchical preconditioning for the stochastic Galerkin method: Upper bounds to the strengthened CBS constants

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10334597" target="_blank" >RIV/00216208:11320/16:10334597 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21110/16:00235797
Result on the web
<a href="http://dx.doi.org/10.1016/j.camwa.2016.01.006" target="_blank" >http://dx.doi.org/10.1016/j.camwa.2016.01.006</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.camwa.2016.01.006" target="_blank" >10.1016/j.camwa.2016.01.006</a>

Result language
angličtina
Original language name
Hierarchical preconditioning for the stochastic Galerkin method: Upper bounds to the strengthened CBS constants
Original language description
One of the popular methods for numerical solution of partial differential equations with uncertain data is the stochastic Galerkin method, where function spaces used for discretized problems are tensor products of finite element spaces of spatial variables and of sets of polynomials of random variables. Related systems of linear equations are thus usually huge. Studying relations between subspaces of the solution spaces is important for obtaining efficient preconditioning. For a hierarchy of polynomials of random variables we introduce upper bounds to the strengthened Cauchy-Bunyakowsky-Schwarz (CBS) constants with respect to the scalar product defined by the operator of the weak form of the underlying equation. Small values of the CBS constant indicate that certain additive or multiplicative two-by-two block preconditioners reduce enough the condition number of the system. Moreover, we show that a recursive multiplicative two-by-two block preconditioning can be used, resulting in the algebraic multilevel iterative (AMLI) method. We present the conditions under which the AMLI preconditioning is of an optimal order. Numerical experiments confirm the introduced theoretical estimates.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/LL1202" target="_blank" >LL1202: Implicitly constituted material models: from theory through model reduction to efficient numerical methods</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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