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Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters
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SYSNO ASEP 0571877 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters Author(s) Béreš, Michal (UGN-S) ORCID, RID, SAI Number of authors 1 Source Title Programs and Algorithms of Numerical Mathematics 21 : Proceedings of Seminar. - Praha : Institute of Mathematics CAS Prague, 2023 / Chleboun J. ; Kůs P. ; Papež J. ; Rozložník M. ; Segeth K. ; Šístek J. - ISBN 978-80-85823-73-8 Pages s. 15-24 Number of pages 10 s. Publication form Online - E Action Programs and Algorithms of Numerical Mathematics /21./ Event date 19.06.2022 - 24.06.2022 VEvent location Jablonec nad Nisou Country CZ - Czech Republic Event type EUR Language eng - English Country CZ - Czech Republic Keywords stochastic Galerkin method ; reduced basis method ; Monte Carlo method ; deflated conjugate gradient method Subject RIV BA - General Mathematics OECD category Applied mathematics R&D Projects TK02010118 GA TA ČR - Technology Agency of the Czech Republic (TA ČR) Institutional support UGN-S - RVO:68145535 DOI 10.21136/panm.2022.02 Annotation In this contribution, we present a solution to the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with uncertain material coefficients in the separable form. The SG system of equations is kept in the compressed tensor form and its solution is a very challenging task. Here, we present the reduced basis (RB) method as a solver which looks for a low-rank representation of the solution. The construction of the RB consists of iterative expanding of the basis using Monte Carlo sampling. We discuss the setting of the sampling procedure and an efficient solution of multiple similar systems emerging during the sampling procedure using deflation. We conclude with a demonstration of the use of SG solution for forward uncertainty quantification. Workplace Institute of Geonics Contact Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Year of Publishing 2024 Electronic address https://dml.cz/bitstream/handle/10338.dmlcz/703184/PANM_21-2022-1_5.pdf
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