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A Deluxe FETI-DP Method for Full DG Discretization of Elliptic Problems

  • Maksymilian Dryja
  • Juan Galvis
  • Marcus Sarkis
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)

Abstract

In this paper we consider a boundary value problem for elliptic second order partial differential equations with highly discontinuous coefficients in a 2D polygonal region Ω. The problem is discretized by a (full) DG method on triangular elements using the space of piecewise linear functions. The goal of this paper is to study a special version of FETI-DP preconditioner, called deluxe, for the resulting discrete system of this discretization. The deluxe version for continuous FE discretization is considered in [1], for standard FETI-DP methods for composite DG method, see [4], for full DG, see [4], and for conforming FEM, see the book [5].

Notes

Acknowledgement

The authors thank the anonymous referee for his suggestions that helped to improve the paper.

This research was supported in part by the Polish Sciences Foundation under grant 2011/01/B/ST1/01179 (Maksymilian Dryja).

References

  1. 1.
    C.R. Dohrmann, O.B. Widlund, Some recent tools and a BDDC algorithm for 3D problems in H(curl), in Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computer Science Engineering, vol. 91 (Springer, New York, 2013), pp. 15–25Google Scholar
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    M. Dryja, M. Sarkis, 3-D FETI-DP preconditioners for composite finite element-discontinuous Galerkin methods, in Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computer Science Engineering, vol. 99 (Springer, Heidelberg, 2014), pp. 127–140Google Scholar
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    M. Dryja, J. Galvis, M. Sarkis, A FETI-DP preconditioner for a composite finite element and discontinuous Galerkin method. SIAM J. Numer. Anal. 51(1), 400–422 (2013)MathSciNetCrossRefMATHGoogle Scholar
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    M. Dryja, J. Galvis, M. Sarkis, The analysis of FETI-DP preconditioner for full DG discretization of elliptic problems in two dimensions, (Springer Berlin Heidelberg, 2015), pp. 1–34 [ISSN 0029-599X]. doi:10.1007/s00211-015-0705-x. http://dx.doi.org/10.1007/s00211-015-0705-x
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    A. Toselli, O. Widlund, Domain Decomposition Methods—Algorithms and Theory. Springer Series in Computational Mathematics, vol. 34 (Springer, Berlin, 2005) [ISBN 3-540-20696-5]Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Maksymilian Dryja
    • 1
  • Juan Galvis
    • 2
  • Marcus Sarkis
    • 3
    • 4
  1. 1.Department of MathematicsWarsaw UniversityWarsawPoland
  2. 2.Departamento de MatemáticasUniversidad Nacional de ColombiaBogotáColombia
  3. 3.Instituto Nacional de Matemática Pura e Aplicada (IMPA)Estrada Dona Castorina 110Rio de JaneiroBrazil
  4. 4.Department of Mathematical Sciences at Worcester Polytechnic InstituteWorcesterUSA

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