BDDC Deluxe for Isogeometric Analysis

  • L. Beirão da Veiga
  • L. F. Pavarino
  • S. Scacchi
  • O. B. Widlund
  • S. Zampini
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)


The main goal of this paper is to design, analyze, and test a BDDC (Balancing Domain Decomposition by Constraints, see [12, 23]) preconditioner for Isogeometric Analysis (IGA), based on a novel type of interface averaging, which we will denote by deluxe scaling, with either full or reduced set of primal constraints. IGA is an innovative numerical methodology, introduced in [17] and first analyzed in [1], where the geometry description of the PDE domain is adopted from a Computer Aided Design (CAD) parametrization usually based on Non-Uniform Rational B-Splines (NURBS) and the same NURBS basis functions are also used as the PDEs discrete basis, following an isoparametric paradigm; see the monograph [10]. Recent works on IGA preconditioners have focused on overlapping Schwarz preconditioners [3, 5, 7, 9], multigrid methods [16], and non-overlapping preconditioners [4, 8, 20].


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • L. Beirão da Veiga
    • 1
  • L. F. Pavarino
    • 1
  • S. Scacchi
    • 1
  • O. B. Widlund
    • 2
  • S. Zampini
    • 3
  1. 1.Dipartimento di MatematicaUniversità di MilanoMilanoItaly
  2. 2.Courant Institute of Mathematical SciencesNew YorkUSA
  3. 3.Extreme Computing Research CenterKing Abdullah University of Science and TechnologyThuwalSaudi Arabia

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