Efficient Solution of Stochastic Galerkin Matrix Equations via Reduced Basis and Tensor Train Approximation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F24%3A00586684" target="_blank" >RIV/68145535:_____/24:00586684 - isvavai.cz</a>
Alternative codes found
RIV/61989100:27240/24:10257007
Result on the web
<a href="https://link.springer.com/book/10.1007/978-3-031-56208-2" target="_blank" >https://link.springer.com/book/10.1007/978-3-031-56208-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-031-56208-2_20" target="_blank" >10.1007/978-3-031-56208-2_20</a>
Alternative languages
Result language
angličtina
Original language name
Efficient Solution of Stochastic Galerkin Matrix Equations via Reduced Basis and Tensor Train Approximation
Original language description
This contribution focuses on the development of a computational method to efficiently solve matrix equations arising from stochastic Galerkin (SG) discretization of steady Darcy flow problems with uncertain and separable permeability fields. The proposed method consists of a two-step solution process. Firstly, we construct a reduced basis for the finite element portion of the discretization using the Monte Carlo (MC) method. We consider various sampling techniques for the MC method. Secondly, we use a tensor polynomial basis to handle the stochastic aspect of the problem and employ a tensor-train (TT) approximation to approximate the overall solution of the reduced SG system. To enhance the convergence of the TT approximation, we use an implicitly preconditioned system with a Kronecker-type preconditioner. Moreover, we also develop low-cost error indicators to assess the accuracy of both thereduced basis and the final solution of the reduced system.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Large-Scale Scientific Computations
ISBN
978-3-031-56207-5
ISSN
0302-9743
e-ISSN
1611-3349
Number of pages
10
Pages from-to
205-214
Publisher name
Springer Nature Switzerland AG
Place of publication
Cham
Event location
Sozopol
Event date
Jun 5, 2023
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
001279202200021