An overlapping Schwarz method for virtual element discretizations in two dimensions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00505500" target="_blank" >RIV/67985840:_____/19:00505500 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.camwa.2018.10.043" target="_blank" >http://dx.doi.org/10.1016/j.camwa.2018.10.043</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.camwa.2018.10.043" target="_blank" >10.1016/j.camwa.2018.10.043</a>

Jazyk výsledku

angličtina

Název v původním jazyce

An overlapping Schwarz method for virtual element discretizations in two dimensions

Popis výsledku v původním jazyce

A new coarse space for domain decomposition methods is presented for nodal elliptic problems in two dimensions. The coarse space is derived from the novel virtual element methods and therefore can accommodate quite irregular polygonal subdomains. It has the advantage with respect to previous studies that no discrete harmonic extensions are required. The virtual element method allows us to handle polygonal meshes and the algorithm can then be used as a preconditioner for linear systems that arise from a discretization with such triangulations. A bound is obtained for the condition number of the preconditioned system by using a two-level overlapping Schwarz algorithm, but the coarse space can also be used for different substructuring methods. This bound is independent of jumps in the coefficient across the interface between the subdomains. Numerical experiments that verify the result are shown, including some with triangular, square, hexagonal and irregular elements and with irregular subdomains obtained by a mesh partitioner.

Název v anglickém jazyce

An overlapping Schwarz method for virtual element discretizations in two dimensions

Popis výsledku anglicky

A new coarse space for domain decomposition methods is presented for nodal elliptic problems in two dimensions. The coarse space is derived from the novel virtual element methods and therefore can accommodate quite irregular polygonal subdomains. It has the advantage with respect to previous studies that no discrete harmonic extensions are required. The virtual element method allows us to handle polygonal meshes and the algorithm can then be used as a preconditioner for linear systems that arise from a discretization with such triangulations. A bound is obtained for the condition number of the preconditioned system by using a two-level overlapping Schwarz algorithm, but the coarse space can also be used for different substructuring methods. This bound is independent of jumps in the coefficient across the interface between the subdomains. Numerical experiments that verify the result are shown, including some with triangular, square, hexagonal and irregular elements and with irregular subdomains obtained by a mesh partitioner.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Computers & Mathematics With Applications

ISSN

0898-1221

e-ISSN

—

Svazek periodika

77

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

15

Strana od-do

1163-1177

Kód UT WoS článku

000459529100017

EID výsledku v databázi Scopus

2-s2.0-85056497711