Eleftherios Soulas and Dennis Shasha

Online Machine Learning Algorithms For Currency Exchange Prediction

Abstract:

A BDDC (Balancing Domain Decomposition by Constraints) preconditioner with a novel scaling, introduced by Dohrmann for problems with more than one variable coeffcient 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 rho- 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 coeffcient 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.