Block Preconditioning of Stochastic Galerkin Problems: New Two-sided Guaranteed Spectral Bounds

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F20%3A00520906" target="_blank" >RIV/68145535:_____/20:00520906 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21110/20:00337145 RIV/71226401:_____/20:N0100313

Výsledek na webu

<a href="https://doi.org/10.1137/19M125902X" target="_blank" >https://doi.org/10.1137/19M125902X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/19M125902X" target="_blank" >10.1137/19M125902X</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Block Preconditioning of Stochastic Galerkin Problems: New Two-sided Guaranteed Spectral Bounds

Popis výsledku v původním jazyce

The paper focuses on numerical solution of parametrized diffusion equations with scalar parameter-dependent coefficient function by the stochastic (spectral) Galerkin method. We study preconditioning of the related discretized problems using preconditioners obtained by modifying the stochastic part of the partial differential equation. We present a simple but general approach for obtaining two-sided bounds to the spectrum of the resulting matrices, based on a particular splitting of the discretized operator. Using this tool and considering the stochastic approximation space formed by classical orthogonal polynomials, we obtain new spectral bounds depending solely on the properties of the coefficient function and the type of the approximation polynomials for several classes of block-diagonal preconditioners. These bounds are guaranteed and applicable to various distributions of parameters. Moreover, the conditions on the parameter-dependent coefficient function are only local, and therefore less restrictive than those usually assumed in the literature.

Název v anglickém jazyce

Block Preconditioning of Stochastic Galerkin Problems: New Two-sided Guaranteed Spectral Bounds

Popis výsledku anglicky

The paper focuses on numerical solution of parametrized diffusion equations with scalar parameter-dependent coefficient function by the stochastic (spectral) Galerkin method. We study preconditioning of the related discretized problems using preconditioners obtained by modifying the stochastic part of the partial differential equation. We present a simple but general approach for obtaining two-sided bounds to the spectrum of the resulting matrices, based on a particular splitting of the discretized operator. Using this tool and considering the stochastic approximation space formed by classical orthogonal polynomials, we obtain new spectral bounds depending solely on the properties of the coefficient function and the type of the approximation polynomials for several classes of block-diagonal preconditioners. These bounds are guaranteed and applicable to various distributions of parameters. Moreover, the conditions on the parameter-dependent coefficient function are only local, and therefore less restrictive than those usually assumed in the literature.

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

SIAM/ASA Journal on Uncertainty Quantification

ISSN

2166-2525

e-ISSN

—

Svazek periodika

8

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

26

Strana od-do

88-113

Kód UT WoS článku

000551383300004

EID výsledku v databázi Scopus

2-s2.0-85085289950