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

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

Authors

Paola F. Antonietti paola.antonietti@polimi.it

Stefano Giani stefano.giani@durham.ac.uk

Paul Houston Paul.Houston@nottingham.ac.uk



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.

Journal Article Type Article
Publication Date Jul 1, 2014
Journal Journal of Scientific Computing
Print ISSN 0885-7474
Electronic ISSN 0885-7474
Publisher Humana Press
Peer Reviewed Peer Reviewed
Volume 60
Issue 1
APA6 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), doi:10.1007/s10915-013-9792-y
DOI https://doi.org/10.1007/s10915-013-9792-y
Keywords Composite finite element methods, Discontinuous Galerkin methods, Domain decomposition, Schwarz preconditioners
Publisher URL http://link.springer.com/article/10.1007%2Fs10915-013-9792-y
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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