Isogeometric BDDC Preconditioning with Deluxe Scaling

A balancing domain decomposition by constraints (BDDC) preconditioner with a novel scaling, introduced by Dohrmann for problems with more than one variable coefficient and here denoted as deluxe scaling, is extended to isogeometric analysis of scalar elliptic problems. This new scaling turns out to be more powerful than the standard ?- and stiffness scalings considered in a previous isogeometric BDDC study. Our h-analysis shows that the condition number of the resulting deluxe BDDC preconditioner is scalable with a quasi-optimal polylogarithmic bound which is also independent of coefficient discontinuities across subdomain interfaces. Extensive numerical experiments support the theory and show that the deluxe scaling yields a remarkable improvement over the older scalings, in particular for large isogeometric polynomial degree and high regularity

Quasi-optimality of BDDC Methods for MITC Reissner-Mindlin Problems

The goal of this paper is to improve a condition number bound proven in [5] for a Balancing Domain DecompositionMethod by Constraints (BDDC) for the Reissner- Mindlin plate bending problem discretized with MITC elements. This BDDC preconditioner is based on selecting the plate rotations and deflection degrees of freedom at the subdomain vertices as primal continuity constraints