An Implementation of a Coarse-Fine Mesh Stabilized Schwarz Method for a Three-Space Dimensional PDE-Problem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F24%3A00586682" target="_blank" >RIV/68145535:_____/24:00586682 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/book/10.1007/978-3-031-56208-2" target="_blank" >https://link.springer.com/book/10.1007/978-3-031-56208-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-56208-2_1" target="_blank" >10.1007/978-3-031-56208-2_1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

An Implementation of a Coarse-Fine Mesh Stabilized Schwarz Method for a Three-Space Dimensional PDE-Problem

Popis výsledku v původním jazyce

When solving very large scale problems on parallel computer platforms, we consider the advantages of domain decomposition in strips or layers, compared to general domain decomposition splitting techniques. The layer sub-domains are grouped in pairs, ordered as odd-even respectively even-odd and solved by a Schwarz alternating iteration method, where the solution at the middle interfaces of the odd-even groups is used as Dirichlet boundary conditions for the even-odd ordered groups and vice versa. To stabilize the method the commonly used coarse mesh method can be replaced by a coarse-fine mesh method. A component analysis of the arising eigenvectors demonstrates that this solution framework leads to very few Schwarz iterations. The resulting coarse-fine mesh method entails a coarse mesh of a somewhat large size. In this study it is solved by two methods, a modified Cholesky factorization of the whole coarse mesh matrix and a block-diagonal preconditioner, based on the coarse mesh points and the inner node points. Extensive numerical tests show that the latter method, being also computationally cheaper, needs very few iterations, in particular when the domain has been divided in many layers and the coarse to fine mesh size ratio is not too large.

Název v anglickém jazyce

An Implementation of a Coarse-Fine Mesh Stabilized Schwarz Method for a Three-Space Dimensional PDE-Problem

Popis výsledku anglicky

When solving very large scale problems on parallel computer platforms, we consider the advantages of domain decomposition in strips or layers, compared to general domain decomposition splitting techniques. The layer sub-domains are grouped in pairs, ordered as odd-even respectively even-odd and solved by a Schwarz alternating iteration method, where the solution at the middle interfaces of the odd-even groups is used as Dirichlet boundary conditions for the even-odd ordered groups and vice versa. To stabilize the method the commonly used coarse mesh method can be replaced by a coarse-fine mesh method. A component analysis of the arising eigenvectors demonstrates that this solution framework leads to very few Schwarz iterations. The resulting coarse-fine mesh method entails a coarse mesh of a somewhat large size. In this study it is solved by two methods, a modified Cholesky factorization of the whole coarse mesh matrix and a block-diagonal preconditioner, based on the coarse mesh points and the inner node points. Extensive numerical tests show that the latter method, being also computationally cheaper, needs very few iterations, in particular when the domain has been divided in many layers and the coarse to fine mesh size ratio is not too large.

Druh

D - Stať ve sborníku

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 statě ve sborníku

Large-Scale Scientific Computations

ISBN

978-3-031-56207-5

ISSN

0302-9743

e-ISSN

1611-3349

Počet stran výsledku

16

Strana od-do

3-18

Název nakladatele

Springer Nature Switzerland AG

Místo vydání

Cham

Místo konání akce

Sozopol

Datum konání akce

5. 6. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001279202200001