BDDC and FETI-DP under Minimalist Assumptions

Files
Links to Files
https://link.springer.com/article/10.1007/s00607-007-0254-yPermanent Link
http://hdl.handle.net/11603/23373Collections
Metadata
Show full item recordAuthor/Creator ORCID
Date
2007-11-30Type of Work
11 pagesText
journal articles
postprints
Citation of Original Publication
Mandel, J., Sousedík, B. BDDC and FETI-DP under minimalist assumptions. Computing 81, 269–280 (2007). https://doi.org/10.1007/s00607-007-0254-yRights
This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.Abstract
The FETI-DP, BDDC and P-FETI-DP preconditioners are derived in a particulary simple
abstract form. It is shown that their properties can be obtained from only on a very small set of
algebraic assumptions. The presentation is purely algebraic and it does not use any particular
definition of method components, such as substructures and coarse degrees of freedom. It is
then shown that P-FETI-DP and BDDC are in fact the same. The FETI-DP and the BDDC
preconditioned operators are of the same algebraic form, and the standard condition number
bound carries over to arbitrary abstract operators of this form. The equality of eigenvalues of
BDDC and FETI-DP also holds in the minimalist abstract setting. The abstract framework is
explained on a standard substructuring example.