Efficient iteration methods for complex systems with an indefinite matrix term

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F22%3A00555974" target="_blank" >RIV/68145535:_____/22:00555974 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s10092-022-00461-w" target="_blank" >https://link.springer.com/article/10.1007/s10092-022-00461-w</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10092-022-00461-w" target="_blank" >10.1007/s10092-022-00461-w</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Efficient iteration methods for complex systems with an indefinite matrix term

Popis výsledku v původním jazyce

Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with symmetric positive definite matrices can be solved readily by rewriting the complex matrix system in two-by-two block matrix form with real matrices which can be efficiently solved by iteration using the preconditioned square block (PRESB) preconditioning method and preferably accelerated by the Chebyshev method. The appearances of an indefinite matrix term causes however some difficulties. To handle this we propose different forms of matrix splitting methods, with or without any parameters involved. A matrix spectral analyses is presented followed by extensive numerical comparisons of various forms of the methods.

Název v anglickém jazyce

Efficient iteration methods for complex systems with an indefinite matrix term

Popis výsledku anglicky

Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with symmetric positive definite matrices can be solved readily by rewriting the complex matrix system in two-by-two block matrix form with real matrices which can be efficiently solved by iteration using the preconditioned square block (PRESB) preconditioning method and preferably accelerated by the Chebyshev method. The appearances of an indefinite matrix term causes however some difficulties. To handle this we propose different forms of matrix splitting methods, with or without any parameters involved. A matrix spectral analyses is presented followed by extensive numerical comparisons of various forms of the methods.

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

2022

Kód důvěrnosti údajů

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

Název periodika

Calcolo

ISSN

0008-0624

e-ISSN

1126-5434

Svazek periodika

59

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

IT - Italská republika

Počet stran výsledku

18

Strana od-do

15

Kód UT WoS článku

000767202400001

EID výsledku v databázi Scopus

2-s2.0-85126258418