Original title: Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters
Authors: Béreš, Michal
Document type: Papers
Conference/Event: Programs and Algorithms of Numerical Mathematics /21./, Jablonec nad Nisou (CZ), 20220619
Year: 2023
Language: eng
Abstract: 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.
Keywords: deflated conjugate gradient method; Monte Carlo method; reduced basis method; stochastic Galerkin method
Project no.: TK02010118
Funding provider: GA TA ČR
Host item entry: Programs and Algorithms of Numerical Mathematics 21 : Proceedings of Seminar, ISBN 978-80-85823-73-8

Institution: Institute of Geonics AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: https://dml.cz/bitstream/handle/10338.dmlcz/703184/PANM_21-2022-1_5.pdf
Original record: https://hdl.handle.net/11104/0342775

Permalink: http://www.nusl.cz/ntk/nusl-524976


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