L. Beirao Da Veiga, L. F. Pavarino, S. Scacchi, O. B. Widlund and S. Zampini
Journal of Scientific Computing, (2016)
Domain decomposition, BDDC deluxe preconditioners, Isogeometric analysis, adaptive primal constraints, elliptic problems
Isogeometric analysis has been introduced as an alternative to nite element methods in order to simplify the integration of CAD software and the discretization of variational problems of continuum mechanics. In contrast with the nite element case, the basis functions of isogeometric analysis are often not nodal. As a consequence, there are fat interfaces which can easily lead to an increase in the number of interface variables after a decomposition of the parameter space into subdomains. Building on earlier work on the deluxe version of the BDDC family of domain decomposition algorithms, several adaptive algorithms are here developed for scalar elliptic problems in an e ort to decrease the dimension of the global, coarse component of these preconditioners. Numerical experiments provide evidence that this work can be successful, yielding scalable and quasi-optimal
adaptive BDDC algorithms for isogeometric discretizations.