Fitted norm preconditioners for the Hodge-Laplacian in mixed form

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F25%3A00642860" target="_blank" >RIV/68145535:_____/25:00642860 - isvavai.cz</a>

Výsledek na webu

<a href="https://articles.math.cas.cz/10.21136/AM.2025.0185-25" target="_blank" >https://articles.math.cas.cz/10.21136/AM.2025.0185-25</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21136/AM.2025.0185-25" target="_blank" >10.21136/AM.2025.0185-25</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Fitted norm preconditioners for the Hodge-Laplacian in mixed form

Popis výsledku v původním jazyce

We use the practical framework for abstract perturbed saddle-point problems recently introduced by Hong et al. to analyze the mixed formulation of the Hodge-Laplace problem on a Hilbert complex. We compose two parameter-dependent norms in which the uniform continuity and stability of the problem follow. This not only guarantees the well-posedness of the corresponding variational formulation on the continuous level, but also of related compatible discrete models. We further simplify the obtained norms and, in both cases, arrive at the same norm-equivalent preconditioner that is easily implementable. The efficiency and uniformity of the preconditioner are demonstrated numerically by the fast convergence and uniformly bounded number of preconditioned MinRes iterations required to solve various instances of Hodge-Laplace problems in two and three space dimensions.

Název v anglickém jazyce

Fitted norm preconditioners for the Hodge-Laplacian in mixed form

Popis výsledku anglicky

We use the practical framework for abstract perturbed saddle-point problems recently introduced by Hong et al. to analyze the mixed formulation of the Hodge-Laplace problem on a Hilbert complex. We compose two parameter-dependent norms in which the uniform continuity and stability of the problem follow. This not only guarantees the well-posedness of the corresponding variational formulation on the continuous level, but also of related compatible discrete models. We further simplify the obtained norms and, in both cases, arrive at the same norm-equivalent preconditioner that is easily implementable. The efficiency and uniformity of the preconditioner are demonstrated numerically by the fast convergence and uniformly bounded number of preconditioned MinRes iterations required to solve various instances of Hodge-Laplace problems in two and three space dimensions.

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

2025

Kód důvěrnosti údajů

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

Název periodika

Applications of Mathematics

ISSN

0862-7940

e-ISSN

1572-9109

Svazek periodika

70

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

21

Strana od-do

907-927

Kód UT WoS článku

001638940400009

EID výsledku v databázi Scopus

2-s2.0-105024748284