Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters

0571877 - ÚGN 2024 RIV CZ eng C - Conference Paper (international conference)
Béreš, Michal
Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters.
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.), s. 15-24. ISBN 978-80-85823-73-8.
[Programs and Algorithms of Numerical Mathematics /21./. Jablonec nad Nisou (CZ), 19.06.2022-24.06.2022]
R&D Projects: GA TA ČR(CZ) TK02010118
Institutional support: RVO:68145535
Keywords : stochastic Galerkin method * reduced basis method * Monte Carlo method * deflated conjugate gradient method
OECD category: Applied mathematics
https://dml.cz/bitstream/handle/10338.dmlcz/703184/PANM_21-2022-1_5.pdf

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.
Permanent Link: https://hdl.handle.net/11104/0342775