Bounds on the spectra of Schur complements of large H-TFETI-DP clusters for 2D Laplacian

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F21%3A10248068" target="_blank" >RIV/61989100:27240/21:10248068 - isvavai.cz</a>

Alternative codes found

RIV/61989100:27740/21:10248068

Result on the web

<a href="https://onlinelibrary.wiley.com/doi/10.1002/nla.2344" target="_blank" >https://onlinelibrary.wiley.com/doi/10.1002/nla.2344</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/nla.2344" target="_blank" >10.1002/nla.2344</a>

Result language

angličtina

Original language name

Bounds on the spectra of Schur complements of large H-TFETI-DP clusters for 2D Laplacian

Original language description

Bounds on the spectrum of Schur complements of subdomain stiffness matrices of the discretized Laplacian with respect to interior variables are important in the convergence analysis of finite element tearing and interconnecting (FETI)-based domain decomposition methods. Here, we are interested in bounds on the regular condition number of Schur complements of &quot;floating&quot; clusters, that is, of matrices comprising the Schur complements of subdomains with prescribed zero Neumann conditions that are joined on the primal level by edge averages. Using some known results, angles of subspaces, and known bounds on the spectrum of Schur complements associated with square domains, we give bounds on the regular condition number of the Schur complement of some &quot;floating&quot; clusters arising from the discretization and decomposition of 2D Laplacian on domains comprising square subdomains. The results show that the condition number of the cluster defined on a fixed domain decomposed into m x m square subdomains joined by edge averages increases proportionally to m. The estimates are compared with numerical values and used in the analysis of H-FETI-DP methods. Though the research has been motivated by an effort to extend the scope of scalability of FETI-based solvers to variational inequalities, the experiments indicate that H-TFETI-DP with large clusters can be useful for the solution of huge linear elliptic problems discretized by sufficiently regular grids.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

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

Publication year

2021

Confidentiality

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

Name of the periodical

Numerical Linear Algebra with Applications

ISSN

1070-5325

e-ISSN

1099-1506

Volume of the periodical

28

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

15

Pages from-to

nestrankovano

UT code for WoS article

000584412900001

EID of the result in the Scopus database

2-s2.0-85093963920