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

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/61989100:27240/20:10244839

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Applications of Mathematics

ISSN

0862-7940

e-ISSN

—

Svazek periodika

65

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

35

Strana od-do

191-225

Kód UT WoS článku

000525004700005

EID výsledku v databázi Scopus

2-s2.0-85083344352