Isogeometric BDDC preconditioners with deluxe scaling (Q2878946)

The main goal of the paper is to design, analyze, and test a balancing domain decomposition by constraints (BDDC) preconditioner for IGA based on a novel type of interface averaging, which is denote by deluxe scaling. This new scaling turns out to be much more powerful than the standard \(\rho\)- and stiffness scalings considered in a previous isogeometric BDDC study. The main result of \(h\)-analysis shows that the condition number of deluxe BDDC preconditioner satisfies the same quasi-optimal polylogarithmic bound in the ratio \(H/h\) of subdomains to elements diameters and that it is independent of the number of subdomains and jumps of the coefficients of elliptic problem across subdomanins interfaces. 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.