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

Béreš, Michal. "Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2023. 15-24. <http://eudml.org/doc/299018>.

@inProceedings{Béreš2023,
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.},
author = {Béreš, Michal},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {stochastic Galerkin method; reduced basis method; Monte Carlo method; deflated conjugate gradient method},
location = {Prague},
pages = {15-24},
publisher = {Institute of Mathematics CAS},
title = {Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters},
url = {http://eudml.org/doc/299018},
year = {2023},
}

TY - CLSWK
AU - Béreš, Michal
TI - Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2023
CY - Prague
PB - Institute of Mathematics CAS
SP - 15
EP - 24
AB - 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.
KW - stochastic Galerkin method; reduced basis method; Monte Carlo method; deflated conjugate gradient method
UR - http://eudml.org/doc/299018
ER -