Two-level Schwarz methods for hybridizable discontinuous Galerkin methods

• Verfasst von: Lu, Peipei [VerfasserIn]
• Verfasst von: Rupp, Andreas [VerfasserIn]
• Verfasst von: Kanschat, Guido [VerfasserIn]
• Titel: Two-level Schwarz methods for hybridizable discontinuous Galerkin methods
• Verf.angabe: Peipei Lu, Andreas Rupp, Guido Kanschat
• E-Jahr: 2023
• Jahr: 15 February 2023
• Umfang: 16 S.
• Fussnoten: Gesehen am 28.03.2023
• Titel Quelle: Enthalten in: Journal of scientific computing
• Ort Quelle: New York, NY [u.a.] : Springer Science + Business Media B.V., 1986
• Jahr Quelle: 2023
• Band/Heft Quelle: 95(2023) vom: Feb., Artikel-ID 9, Seite 1-16
• ISSN Quelle: 1573-7691
• DOI: doi:10.1007/s10915-023-02121-9
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 65F10
• Sach-SW: 65N30
• Sach-SW: 65N50
• Sach-SW: Additive schwarz
• Sach-SW: HDG
• Sach-SW: Multigrid
• Sach-SW: Preconditioner
• K10plus-PPN: 1840300272

Abstract

In this paper, we propose two-level domain decomposition methods for hybridizable discontinuous Galerkin discretizations including hybridized local discontinuous Galerkin, Raviart-Thomas, and Brezzi-Douglas-Marini finite elements for Poisson’s equation. We study the additive Schwarz method as a preconditioner and the multiplicative method as an iterative solver. In our algorithm, the same discretization scheme is defined on the coarse mesh. In particular, we use the injection operator developed in [13] and prove that the condition number of the preconditioned system only depends on the fraction between coarse and fine mesh sizes and the overlap width. Numerical experiments underline our analytical findings.