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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F23%3A00571877" target="_blank" >RIV/68145535:_____/23:00571877 - isvavai.cz</a>
Alternative codes found
RIV/61989100:27240/23:10257405
Result on the web
<a href="https://dml.cz/bitstream/handle/10338.dmlcz/703184/PANM_21-2022-1_5.pdf" target="_blank" >https://dml.cz/bitstream/handle/10338.dmlcz/703184/PANM_21-2022-1_5.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/panm.2022.02" target="_blank" >10.21136/panm.2022.02</a>

Result language
angličtina
Original language name
Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters
Original language description
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.
Czech name
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Czech description
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Project
<a href="/en/project/TK02010118" target="_blank" >TK02010118: Prediction of Excavation Damage Zone properties for safety and reliability of a deep geological repository.</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Programs and Algorithms of Numerical Mathematics 21 : Proceedings of Seminar
ISBN
978-80-85823-73-8
ISSN
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e-ISSN
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Number of pages
10
Pages from-to
15-24
Publisher name
Institute of Mathematics CAS Prague
Place of publication
Praha
Event location
Jablonec nad Nisou
Event date
Jun 19, 2022
Type of event by nationality
EUR - Evropská akce
UT code for WoS article
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