How does the partition of unity influence SORAS preconditioner?

We investigate the influence of the choice of the partition of unity on the convergence of the Symmetrized Optimized Restricted Additive Schwarz (SORAS) preconditioner for the reaction-convection-diffusion equation. We focus on two kinds of partitions of unity, and study the dependence on the overla...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Bonazzoli, Marcella, Claeys, Xavier, Nataf, Frédéric, Pierre-Henri Tournier
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 24.04.2023
Subjects:	Convection-diffusion equation Unity
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	We investigate the influence of the choice of the partition of unity on the convergence of the Symmetrized Optimized Restricted Additive Schwarz (SORAS) preconditioner for the reaction-convection-diffusion equation. We focus on two kinds of partitions of unity, and study the dependence on the overlap and on the number of subdomains. In particular, the second kind of partition of unity, which is non-zero in the interior of the whole overlapping region, gives more favorable convergence properties, especially when increasing the overlap width, in comparison with the first kind of partition of unity, whose gradient is zero on the subdomain interfaces and which would be the natural choice for ORAS solver instead.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2212.03132