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An Efficient Reduced Basis Construction for Stochastic Galerkin Matrix Equations Using Deflated Conjugate Gradients

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    SYSNO ASEP0537200
    Document TypeC - Proceedings Paper (int. conf.)
    R&D Document TypeConference Paper
    TitleAn Efficient Reduced Basis Construction for Stochastic Galerkin Matrix Equations Using Deflated Conjugate Gradients
    Author(s) Béreš, Michal (UGN-S) ORCID, RID, SAI
    Number of authors1
    Source TitleLecture Notes in Electrical Engineering, AETA 2018 - Recent Advances in Electrical Engineering and Related Sciences: Theory and Application, 554. - Cham : Springer Nature Switzerland AG, 2020 / Zelinka I. ; Brandstetter P. ; Trong Dao T. ; Hoang Duy V. ; Kim S. B. - ISSN 1876-1100 - ISBN 978-3-030-14906-2
    Pagess. 175-184
    Number of pages10 s.
    Publication formOnline - E
    ActionInternational Conference on Advanced Engineering Theory and Applications 2018 /5./
    Event date11.11.2018 - 13.11.2018
    VEvent locationOstrava
    CountryCZ - Czech Republic
    Event typeWRD
    Languageeng - English
    CountryCH - Switzerland
    Keywordsstochastic Galerkin method ; reduced basis method ; deflated conjugate gradients method ; darcy flow problem
    Subject RIVBA - General Mathematics
    OECD categoryApplied mathematics
    R&D ProjectsLQ1602 GA MŠMT - Ministry of Education, Youth and Sports (MEYS)
    Institutional supportUGN-S - RVO:68145535
    EID SCOPUS85066301908
    DOI10.1007/978-3-030-14907-9_18
    AnnotationIn this article, we examine an efficient solution of the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with uncertain material parameters on given interfaces. The solution of the SG system of equations, here represented as matrix equations, is usually a very challenging task. A relatively new approach to the solution of the SG matrix equations is the reduced basis (RB) solver, which looks for the low-rank representation of the solution. The construction of the RB is usually done iteratively and consists of multiple solutions of systems of equations. We aim to speed up the process using the deflated conjugate gradients (DCG). Other contributions of this work are a modified specific construction of the RB without the need of Cholesky factor and an adaptive choice of the candidate vectors for the expansion of the RB. The proposed approach allows an efficient parallel implementation
    WorkplaceInstitute of Geonics
    ContactLucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354
    Year of Publishing2021
    Electronic addresshttps://link.springer.com/chapter/10.1007/978-3-030-14907-9_18
Number of the records: 1  

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