Favorable bounds on the spectrum of discretized Steklov-Poincaré operator and applications to domain decomposition methods in 2D

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F24%3A00603564" target="_blank" >RIV/68145535:_____/24:00603564 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.camwa.2024.04.033" target="_blank" >https://doi.org/10.1016/j.camwa.2024.04.033</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.camwa.2024.04.033" target="_blank" >10.1016/j.camwa.2024.04.033</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Favorable bounds on the spectrum of discretized Steklov-Poincaré operator and applications to domain decomposition methods in 2D

Popis výsledku v původním jazyce

The efficiency of numerical solvers of PDEs depends on the approximation properties of the discretization methods and the conditioning of the resulting linear systems. If applicable, the boundary element methods typically provide better approximation with unknowns limited to the boundary than the Schur complement of the finite element stiffness matrix with respect to the interior variables. Since both matrices correctly approximate the same object, the Steklov-Poincaré operator, it is natural to assume that the matrices corresponding to the same fine boundary discretization are similar. However, this note shows that the distribution of the spectrum of the boundary element stiffness matrix is significantly better conditioned than the finite element Schur complement. The effect of the favorable conditioning of BETI clusters is demonstrated by solving huge problems by H-TBETI-DP and H-TFETI-DP.

Název v anglickém jazyce

Favorable bounds on the spectrum of discretized Steklov-Poincaré operator and applications to domain decomposition methods in 2D

Popis výsledku anglicky

The efficiency of numerical solvers of PDEs depends on the approximation properties of the discretization methods and the conditioning of the resulting linear systems. If applicable, the boundary element methods typically provide better approximation with unknowns limited to the boundary than the Schur complement of the finite element stiffness matrix with respect to the interior variables. Since both matrices correctly approximate the same object, the Steklov-Poincaré operator, it is natural to assume that the matrices corresponding to the same fine boundary discretization are similar. However, this note shows that the distribution of the spectrum of the boundary element stiffness matrix is significantly better conditioned than the finite element Schur complement. The effect of the favorable conditioning of BETI clusters is demonstrated by solving huge problems by H-TBETI-DP and H-TFETI-DP.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

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

1873-7668

Svazek periodika

167

Číslo periodika v rámci svazku

August 2024

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

9

Strana od-do

12-20

Kód UT WoS článku

001242886600001

EID výsledku v databázi Scopus

2-s2.0-85192869860