FETI-DP Preconditioners for the Virtual Element Method on General 2D Meshes

  • Daniele PradaEmail author
  • Silvia Bertoluzza
  • Micol Pennacchio
  • Marco Livesu
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


We analyze the performance of a state-of-the-art domain decomposition approach, the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) method (Toselli and Widlund, Domain decomposition methods—algorithms and theory. Springer series in computational mathematics, vol 34, 2005), for the efficient solution of very large linear systems arising from elliptic problems discretized by the Virtual Element Method (VEM) (Beirão da Veiga et al., Math Models Methods Appl Sci 24:1541–1573, 2014). We provide numerical experiments on a model linear elliptic problem with highly heterogeneous diffusion coefficients on arbitrary Voronoi meshes, which we modify by adding nodes and edges deriving from the intersection with an unrelated coarse decomposition. The experiments confirm also in this case that the FETI-DP method is numerically scalable with respect to both the problem size and number of subdomains, and its performance is robust with respect to jumps in the diffusion coefficients and shape of the mesh elements.



This paper has been realized in the framework of the ERC Project CHANGE, which has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No 694515). The authors would also like to thank the members of the Shapes and Semantics Modeling Group at IMATI-CNR for fruitful discussions on conformal meshing.


  1. 1.
    S. Bertoluzza, M. Pennacchio, D. Prada, BDDC and FETI-DP for the virtual element method. Calcolo 54(4), 1565–1593 (2017)MathSciNetCrossRefGoogle Scholar
  2. 2.
    L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L.D. Marini, A. Russo, Basic principles of virtual element methods. Math. Models Methods Appl. Sci. 23(1), 199–214 (2013)MathSciNetCrossRefGoogle Scholar
  3. 3.
    L. Beirão da Veiga, A. Chernov, L. Mascotto, A. Russo, Basic principles of hp virtual elements on quasiuniform meshes. Math. Models Methods Appl. Sci. 26(8), 1567–1598 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    L. Beirão da Veiga, F. Brezzi, L.D. Marini, A. Russo, Virtual element method for general second-order elliptic problems on polygonal meshes. Math. Models Methods Appl. Sci. 26(4), 729–750 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    L. Beirão da Veiga, F. Brezzi, L.D. Marini, A. Russo, The hitchhiker’s guide to the virtual element method. Math. Models Methods Appl. Sci. 24, 1541–1573 (2014)MathSciNetCrossRefGoogle Scholar
  6. 6.
    A. Toselli, O. Widlund, Domain Decomposition Methods - Algorithms and Theory. Springer Series in Computational Mathematics, vol. 34 (Springer, Berlin, 2005)Google Scholar
  7. 7.
    M. Livesu, CinoLib: a generic programming header only C++ library for processing polygonal and polyhedral meshes (2017).
  8. 8.
    M. Attene, Direct repair of self-intersecting meshes. Graph Models 76(6), 658–668 (2014)CrossRefGoogle Scholar
  9. 9.
    J.R. Shewchuk, Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete Comput. Geom. 18(3), 305–363 (1997)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Daniele Prada
    • 1
    Email author
  • Silvia Bertoluzza
    • 1
  • Micol Pennacchio
    • 1
  • Marco Livesu
    • 1
  1. 1.Istituto di Matematica Applicata e Tecnologie Informatiche del CNRPaviaItaly

Personalised recommendations