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An Efficient Reduced Basis Construction for Stochastic Galerkin Matrix Equations Using Deflated Conjugate Gradients
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SYSNO ASEP 0537200 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title An Efficient Reduced Basis Construction for Stochastic Galerkin Matrix Equations Using Deflated Conjugate Gradients Author(s) Béreš, Michal (UGN-S) ORCID, RID, SAI Number of authors 1 Source Title Lecture 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 Pages s. 175-184 Number of pages 10 s. Publication form Online - E Action International Conference on Advanced Engineering Theory and Applications 2018 /5./ Event date 11.11.2018 - 13.11.2018 VEvent location Ostrava Country CZ - Czech Republic Event type WRD Language eng - English Country CH - Switzerland Keywords stochastic Galerkin method ; reduced basis method ; deflated conjugate gradients method ; darcy flow problem Subject RIV BA - General Mathematics OECD category Applied mathematics R&D Projects LQ1602 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Institutional support UGN-S - RVO:68145535 EID SCOPUS 85066301908 DOI 10.1007/978-3-030-14907-9_18 Annotation In 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 Workplace Institute of Geonics Contact Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Year of Publishing 2021 Electronic address https://link.springer.com/chapter/10.1007/978-3-030-14907-9_18
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