November 20, 2017 14:43 WSPC/INSTRUCTION FILE TR2017-988 Mathematical Models and Methods in Applied Sciences c  World Scientiﬁc Publishing Company Isogeometric BDDC Deluxe preconditioners for linear elasticity L. F. Pavarino ˚ Dipartimento di Matematica, Universit`a degli Studi di Pavia, Via Ferrata 5, 27100 Pavia, Italy. luca.pavarino@unipv.it S. Scacchi ˚ Dipartimento di Matematica, Universit` a degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy. simone.scacchi@unimi.it O. B. Widlund : Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA. widlund@cims.nyu.edu S. Zampini Extreme Computing Research Center, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia. stefano.zampini@kaust.edu.sa TR2017-988 Balancing domain decomposition by constraints (BDDC) preconditioners have been shown to provide rapidly convergent preconditioned conjugate gradient methods for solv- ing many of the very ill-conditioned systems of algebraic equations which often arise in ﬁnite element approximations of a large variety of problems in continuum mechanics. These algorithms have also been developed successfully for problems arising in isogeo- metric analysis. In particular, the BDDC deluxe version has proven very successful for problems approximated by non-uniform rational B-splines (NURBS), even those of high order and regularity. One main purpose of this paper is to extend the theory, previ- ously fully developed only for scalar elliptic problems in the plane, to problems of linear elasticity in three dimensions. Numerical experiments supporting the theory, are also re- ported. Some of these experiments highlight the fact that the development of the theory can help to decrease substantially the dimension of the primal space of the BDDC al- gorithm, which provides the necessary global component of these preconditioners, while maintaining scalability and good convergence rates. Keywords : domain decomposition; BDDC deluxe preconditioners; isogeometric analysis; ˚ This work was supported by grants of M.I.U.R. (PRIN 201289A4LX 002) and of Istituto Nazionale di Alta Matematica (INDAM-GNCS). : This work has been supported by the National Science Foundation Grant DMS-1522736 1