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

Result code in 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>

Alternative codes found

RIV/61989100:27740/24:10254836

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10100 - Mathematics

Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2024

Confidentiality

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

Name of the periodical

Computational Methods in Applied Mathematics

ISSN

1609-4840

e-ISSN

1609-9389

Volume of the periodical

24

Issue of the periodical within the volume

2

Country of publishing house

DE - GERMANY

Number of pages

13

Pages from-to

431-443

UT code for WoS article

001152115000001

EID of the result in the Scopus database

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