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Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains

Antonietti, Paola F.; Giani, Stefano; Houston, Paul

Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains Thumbnail


Authors

Paola F. Antonietti

Stefano Giani

PAUL HOUSTON PAUL.HOUSTON@NOTTINGHAM.AC.UK
Professor of Computational and Applied Maths



Abstract

In this article we consider the application of Schwarz-type domain decomposition preconditioners for discontinuous Galerkin finite element approximations of elliptic partial differential equations posed on complicated domains, which are characterized by small details in the computational domain or microstructures. In this setting, it is necessary to define a suitable coarse-level solver, in order to guarantee the scalability of the preconditioner under mesh refinement. To this end, we exploit recent ideas developed in the so-called composite finite element framework, which allows for the definition of finite element methods on general meshes consisting of agglomerated elements. Numerical experiments highlighting the practical performance of the proposed preconditioner are presented.

Citation

Antonietti, P. F., Giani, S., & Houston, P. (2014). Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains. Journal of Scientific Computing, 60(1), https://doi.org/10.1007/s10915-013-9792-y

Journal Article Type Article
Publication Date Jul 1, 2014
Deposit Date Aug 26, 2015
Publicly Available Date Mar 29, 2024
Journal Journal of Scientific Computing
Print ISSN 0885-7474
Electronic ISSN 0885-7474
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 60
Issue 1
DOI https://doi.org/10.1007/s10915-013-9792-y
Keywords Composite finite element methods, Discontinuous Galerkin methods, Domain decomposition, Schwarz preconditioners
Public URL https://nottingham-repository.worktribe.com/output/994920
Publisher URL http://link.springer.com/article/10.1007%2Fs10915-013-9792-y

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