Isogeometric BDDC Preconditioners with Deluxe Scaling

A BDDC (Balancing Domain Decomposition by Constraints) preconditioner with a novel deluxe scaling, introduced by Dohrmann for problems with more than one variable coefficient, is extended to Isogeometric Analysis of scalar elliptic problems. This new scaling turns out to be much more powerful than BDDC with standard ρand stiffness scaling studied in a previous study of isogeometric BDDC. 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 can yield a remarkable improvement over the older scalings, in particular, for large polynomial degree and high regularity of the isogeometric elements.