Efficient Solution of Stochastic Galerkin Matrix Equations via Reduced Basis and Tensor Train Approximation

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/61989100:27240/24:10257007

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Efficient Solution of Stochastic Galerkin Matrix Equations via Reduced Basis and Tensor Train Approximation

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Efficient Solution of Stochastic Galerkin Matrix Equations via Reduced Basis and Tensor Train Approximation

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název statě ve sborníku

Large-Scale Scientific Computations

ISBN

978-3-031-56207-5

ISSN

0302-9743

e-ISSN

1611-3349

Počet stran výsledku

10

Strana od-do

205-214

Název nakladatele

Springer Nature Switzerland AG

Místo vydání

Cham

Místo konání akce

Sozopol

Datum konání akce

5. 6. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001279202200021