BDDC preconditioners for isogeometric analysis (Q2836493)

The authors consider the model elliptic equation \(-\nabla \cdot(\rho \nabla u)=f\) in \(\Omega\) where \(\rho\) is a scalar field. They propose a nonoverlapping domain decomposition method based on the balancing domain decomposition by constraints (BDDC) preconditioner. In the isogeometric case, the construction of nonoverlapping preconditioners is more challenging because spline basis functions are not nodal and have nonlocal support spanning several elements. The authors construct a BDDC preconditioner by defining primality continuity constraints across a generalized subdomain interface.NEWLINENEWLINEBy constructing appropriate discrete norms, the authors prove that their isogeometric BDDC preconditioner is scalable in the number of subdomains and quasioptimal in the ratio of subdomain and element sizes. Whereas the theoretical results are obtained only for two dimensions, numerical experiments exhibit the validity of these results in two and three dimensions.