Robust PRESB Preconditioning of a 3-Dimensional Space-Time Finite Element Method for Parabolic Problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F24%3A10254836" target="_blank" >RIV/61989100:27240/24:10254836 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27740/24:10254836

Výsledek na webu

<a href="http://homel.vsb.cz/~luk76" target="_blank" >http://homel.vsb.cz/~luk76</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/cmam-2023-0085" target="_blank" >10.1515/cmam-2023-0085</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Robust PRESB Preconditioning of a 3-Dimensional Space-Time Finite Element Method for Parabolic Problems

Popis výsledku v původním jazyce

We present a recently developed preconditioning of square block matrices (PRESB) to be used within a parallel method to solve linear systems of equations arising from tensor-product discretizations of initial boundary-value problems for parabolic partial differential equations. We consider weak formulations in Bochner-Sobolev spaces and tensor-product finite element approximations for the heat and eddy current equations. The fast diagonalization method is employed to decouple the arising linear system of equations into auxiliary spatial complex-valued linear systems that can be solved concurrently. We prove that the real part of the system matrix is positive definite, which allows us to accelerate the flexible generalized minimal residual method (FGMRES) by the PRESB preconditioner. The action of PRESB on a vector includes two solutions with positive definite matrices. The spectrum of the preconditioned system lies between 1/2 and 1. Finally, we combine the PRESB-FGMRES method with multigrid-CG iterations and illustrate the numerical efficiency and the robustness for spatial discretizations up to 12 millions degrees of freedom.

Název v anglickém jazyce

Robust PRESB Preconditioning of a 3-Dimensional Space-Time Finite Element Method for Parabolic Problems

Popis výsledku anglicky

We present a recently developed preconditioning of square block matrices (PRESB) to be used within a parallel method to solve linear systems of equations arising from tensor-product discretizations of initial boundary-value problems for parabolic partial differential equations. We consider weak formulations in Bochner-Sobolev spaces and tensor-product finite element approximations for the heat and eddy current equations. The fast diagonalization method is employed to decouple the arising linear system of equations into auxiliary spatial complex-valued linear systems that can be solved concurrently. We prove that the real part of the system matrix is positive definite, which allows us to accelerate the flexible generalized minimal residual method (FGMRES) by the PRESB preconditioner. The action of PRESB on a vector includes two solutions with positive definite matrices. The spectrum of the preconditioned system lies between 1/2 and 1. Finally, we combine the PRESB-FGMRES method with multigrid-CG iterations and illustrate the numerical efficiency and the robustness for spatial discretizations up to 12 millions degrees of freedom.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10100 - Mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Computational Methods in Applied Mathematics

ISSN

1609-4840

e-ISSN

1609-9389

Svazek periodika

24

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

13

Strana od-do

431-443

Kód UT WoS článku

001152115000001

EID výsledku v databázi Scopus

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