Analysis of the multiplicative Schwarz method for matrices with a special block structure

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10435452" target="_blank" >RIV/00216208:11320/21:10435452 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=OeonpfiKrr" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=OeonpfiKrr</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1553/etna_vol54s31" target="_blank" >10.1553/etna_vol54s31</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Analysis of the multiplicative Schwarz method for matrices with a special block structure

Popis výsledku v původním jazyce

We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for example, when a (partial) differential equation is posed and discretized on a two-dimensional domain that consists of two subdomains with an overlap. This is a basic situation in the context of domain decomposition methods. Our analysis is based on the algebraic structure of the Schwarz iteration matrices, and we derive error bounds that are based on the block diagonal dominance of the given system matrix. Our analysis does not assume that the system matrix is symmetric (positive definite), or has the M-or H-matrix property. Our approach is motivated by, and significantly generalizes, an analysis for a special one-dimensional model problem of Echeverria et al. given in [Electron. Trans. Numer. Anal., 48 (2018), pp. 40-62].

Název v anglickém jazyce

Analysis of the multiplicative Schwarz method for matrices with a special block structure

Popis výsledku anglicky

We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for example, when a (partial) differential equation is posed and discretized on a two-dimensional domain that consists of two subdomains with an overlap. This is a basic situation in the context of domain decomposition methods. Our analysis is based on the algebraic structure of the Schwarz iteration matrices, and we derive error bounds that are based on the block diagonal dominance of the given system matrix. Our analysis does not assume that the system matrix is symmetric (positive definite), or has the M-or H-matrix property. Our approach is motivated by, and significantly generalizes, an analysis for a special one-dimensional model problem of Echeverria et al. given in [Electron. Trans. Numer. Anal., 48 (2018), pp. 40-62].

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

2021

Kód důvěrnosti údajů

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

Název periodika

Electronic Transactions on Numerical Analysis

ISSN

1068-9613

e-ISSN

—

Svazek periodika

54

Číslo periodika v rámci svazku

November 13, 2020

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

31-50

Kód UT WoS článku

000715312600003

EID výsledku v databázi Scopus

2-s2.0-85097229711