document: To the best of authors’ knowledge, so far there are only very few papers [12,13,16,29] which address the performance of linear algebra solvers. In Ref. [16], the authors study the performance of direct solvers which are clearly not suitable for large problems, specially in three-dimensions. In Ref. [29], the tearing and interconnecting approach of finite element methods is used in the context of isogeometric analysis, and the numerical tests (in absence of any theoretical study) suggest almost optimal (with a logarithmic factor) convergence rates of the proposed isogeometric tearing and interconnecting method. The only paper which provides rigorous theoretical study, supported by extensive numerical examples, is by Beirao et al. [12] where the authors discuss the overlapping Schwarz methods. The same authors have also proposed BDDC preconditioners for isogeometric analysis in [13].
doc_bio_tags: O O O O O O O O O O O O O O O O O O B I I I I O O O O O O O B I I I O O O O O O B I O O O O O O O B I I I I I I I O O O O O O B I O O B I O O O O B I O O O O O O O O O O O O B I I I I O O O O O B I I O O B I I O O O O O O O O O O O O B I O O O O O O B I O B I O O
extractive_keyphrases: bddc preconditioners extensive numerical examples isogeometric analysis isogeometric tearing and interconnecting method large problems numerical tests performance of direct solvers performance of linear algebra solvers rigorous theoretical study schwarz methods tearing and interconnecting approach of finite element methods theoretical study