Schur complement spectral bounds for large hybrid FETI-DP clusters and huge three-dimensional scalar problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F21%3A10247608" target="_blank" >RIV/61989100:27240/21:10247608 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27740/21:10247608

Výsledek na webu

<a href="https://www.degruyter.com/document/doi/10.1515/jnma-2020-0048/html" target="_blank" >https://www.degruyter.com/document/doi/10.1515/jnma-2020-0048/html</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/jnma-2020-0048" target="_blank" >10.1515/jnma-2020-0048</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Schur complement spectral bounds for large hybrid FETI-DP clusters and huge three-dimensional scalar problems

Popis výsledku v původním jazyce

Bounds on the spectrum of Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients of the convergence analysis of FETI (finite element tearing and interconnecting) based domain decomposition methods. Here we give bounds on the regular condition number of Schur complements of &quot;floating&quot;clusters arising from the discretization of 3D Laplacian on a cube decomposed into cube subdomains. The results show that the condition number of the cluster defined on a fixed domain decomposed into m x m x m cube subdomains connected by face and optionally edge averages increases proportionally to m. The estimates support scalability of unpreconditioned H-FETI-DP (hybrid FETI dual-primal) method. Though the research is most important for the solution of variational inequalities, the results of numerical experiments indicate that unpreconditioned H-FETI-DP with large clusters can be useful also for the solution of huge linear problems. (C) 2021 Walter de Gruyter GmbH, Berlin/Boston 2021.

Název v anglickém jazyce

Schur complement spectral bounds for large hybrid FETI-DP clusters and huge three-dimensional scalar problems

Popis výsledku anglicky

Bounds on the spectrum of Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients of the convergence analysis of FETI (finite element tearing and interconnecting) based domain decomposition methods. Here we give bounds on the regular condition number of Schur complements of &quot;floating&quot;clusters arising from the discretization of 3D Laplacian on a cube decomposed into cube subdomains. The results show that the condition number of the cluster defined on a fixed domain decomposed into m x m x m cube subdomains connected by face and optionally edge averages increases proportionally to m. The estimates support scalability of unpreconditioned H-FETI-DP (hybrid FETI dual-primal) method. Though the research is most important for the solution of variational inequalities, the results of numerical experiments indicate that unpreconditioned H-FETI-DP with large clusters can be useful also for the solution of huge linear problems. (C) 2021 Walter de Gruyter GmbH, Berlin/Boston 2021.

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

Journal of Numerical Mathematics

ISSN

1570-2820

e-ISSN

1569-3953

Svazek periodika

29

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

18

Strana od-do

289-306

Kód UT WoS článku

000730400000002

EID výsledku v databázi Scopus

2-s2.0-85099927350