Advertisement

Adaptive Deluxe BDDC Mixed and Hybrid Primal Discretizations

  • Alexandre Madureira
  • Marcus SarkisEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 125)

Abstract

Major progress has been made recently to make FETI-DP and BDDC preconditioners robust with respect to any variation of coefficients inside and/or across the subdomains.

Notes

Acknowledgments

The author “A. Madureira” was supported by CNPq/Brazil. The work of “M. Sarkis” was supported by the National Science Foundation Grant DMS-1522663.

References

  1. 1.
    C. Farhat, I. Harari, L.P. Franca, The discontinuous enrichment method. Comput. Methods Appl. Mech. Eng. 190(48), 6455–6479 (2001)MathSciNetCrossRefGoogle Scholar
  2. 2.
    J. Galvis, Y. Efendiev, Domain decomposition preconditioners for multiscale flows in high-contrast media. Multiscale Model. Simul. 8(4), 1461–1483 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    C. Harder, A. Madureira, F. Valentin, A hybrid-mixed method for elasticity. ESAIM Math. Model. Numer. Anal. 50(2), 311–336 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    A. Heinlein, U. Hetmaniuk, A. Klawonn, O. Rheinbach, The approximate component mode synthesis special finite element method in two dimensions: parallel implementation and numerical results. J. Comput. Appl. Math. 289, 116–133 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    T.J.R. Hughes, Multiscale phenomena: green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods. Comput. Methods Appl. Mech. Eng. 127(1–4), 387–401 (1995)MathSciNetCrossRefGoogle Scholar
  6. 6.
    A. Madureira, M. Sarkis, Adaptive ACMS: a robust localized approximated component mode synthesis method. https://arxiv.org/pdf/1709.04044.pdf
  7. 7.
    A. Madureira, M. Sarkis, Hybrid localized spectral decomposition for multiscale problems. https://arxiv.org/pdf/1706.08941.pdf
  8. 8.
    A. Målqvist, P. Henning, F. Hellman, Multiscale mixed finite elements. Discret. Contin. Dyn. Syst. Ser. S 9(5), 1269–1298 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    D.-S. Oh, O.B. Widlund, S. Zampini, C.R. Dohrmann, BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields. Math. Comput. 87, 659–692 (2018)MathSciNetCrossRefGoogle Scholar
  10. 10.
    D. Peterseim, R. Scheichl, Robust numerical upscaling of elliptic multiscale problems at high contrast. Comput. Methods Appl. Math. 16(4), 579–603 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    P.-A. Raviart, J.M. Thomas, Primal hybrid finite element methods for 2nd order elliptic equations. Math. Comput. 31(138), 391–413 (1977)zbMATHGoogle Scholar
  12. 12.
    S. Zampini, X. Tu, Multilevel balancing domain decomposition by constraints deluxe algorithms with adaptive coarse spaces for flow in porous media. SIAM J. Sci. Comput. 39(4), 1389–1415 (2017)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratório Nacional de Computação CientíficaPetrópolisBrazil
  2. 2.Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA

Personalised recommendations