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Journal of Scientific Computing

, Volume 60, Issue 1, pp 203–227 | Cite as

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

  • Paola F. Antonietti
  • Stefano Giani
  • Paul HoustonEmail author
Article

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.

Keywords

Composite finite element methods Discontinuous Galerkin methods  Domain decomposition Schwarz preconditioners 

Notes

Acknowledgments

SG and PH acknowledge the financial support of the EPSRC under the grant EP/H005498. PH also acknowledges the support of the Leverhulme Trust.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Paola F. Antonietti
    • 1
  • Stefano Giani
    • 2
  • Paul Houston
    • 3
    Email author
  1. 1.MOX–Modeling and Scientific Computing, Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.School of Engineering and Computing SciencesDurham UniversityDurhamUK
  3. 3.School of Mathematical SciencesUniversity of NottinghamNottinghamUK

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