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Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains

Antonietti, Paola; Giani, Stefano; Houston, Paul

Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains Thumbnail


Authors

Paola Antonietti

Paul Houston



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., Giani, S., & Houston, P. (2014). Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains. Journal of Scientific Computing, 60(1), 203-227. https://doi.org/10.1007/s10915-013-9792-y

Journal Article Type Article
Acceptance Date Oct 9, 2013
Publication Date Jul 1, 2014
Deposit Date Sep 29, 2014
Publicly Available Date Jun 22, 2015
Journal Journal of Scientific Computing
Print ISSN 0885-7474
Electronic ISSN 1573-7691
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 60
Issue 1
Pages 203-227
DOI https://doi.org/10.1007/s10915-013-9792-y
Keywords Composite finite element methods, Discontinuous Galerkin methods, Domain decomposition, Schwarz preconditioners.

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