A comparison of approaches for the construction of reduced basis for stochastic Galerkin matrix equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F20%3A00534428" target="_blank" >RIV/68145535:_____/20:00534428 - isvavai.cz</a>
Alternative codes found
RIV/61989100:27240/20:10244839
Result on the web
<a href="https://link.springer.com/article/10.21136/AM.2020.0257-19" target="_blank" >https://link.springer.com/article/10.21136/AM.2020.0257-19</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/AM.2020.0257-19" target="_blank" >10.21136/AM.2020.0257-19</a>

Result language
angličtina
Original language name
A comparison of approaches for the construction of reduced basis for stochastic Galerkin matrix equations
Original language description
We examine different approaches to an efficient solution of the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with different, uncertain coefficients in apriori known subdomains. The solution of the SG system of equations is usually a very challenging task. A relatively new approach to the solution of the SG matrix equations is the reduced basis (RB) solver, which looks for a low-rank representation of the solution. The construction of the RB is usually done iteratively and consists of multiple solutions of systems of equations. We examine multiple approaches and their modifications to the construction of the RB, namely the reduced rational Krylov subspace method and Monte Carlo sampling approach. We also aim at speeding up the process using the deflated conjugate gradients (DCG). We test and compare these methods on a set of problems with a varying random behavior of the material on subdomains as well as different geometries of subdomains.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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