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Title: Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters (English)
Author: Béreš, Michal
Language: English
Journal: Programs and Algorithms of Numerical Mathematics
Volume: Proceedings of Seminar. Jablonec nad Nisou, June 19-24, 2022
Issue: 2022
Year:
Pages: 15-24
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Category: math
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Summary: 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. (English)
Keyword: stochastic Galerkin method
Keyword: reduced basis method
Keyword: Monte Carlo method
Keyword: deflated conjugate gradient method
MSC: 65C05
MSC: 65M60
MSC: 65M70
DOI: 10.21136/panm.2022.02
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Date available: 2023-04-13T06:21:10Z
Last updated: 2023-06-05
Stable URL: http://hdl.handle.net/10338.dmlcz/703184
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