On the Equivalence of Primal and Dual Substructuring Preconditioners

Date

2009-09-30

Department

Program

Citation of Original Publication

Sousedik, Bedrich; Mandel, Jan; On the Equivalence of Primal and Dual Substructuring Preconditioners; Electronic Transactions on Numerical Analysis, Volume 31, pp. 384-402, 30 September, 2009; https://etna.math.kent.edu/vol.31.2008/pp384-402.dir/pp384-402.pdf

Rights

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

After a short historical review, we present four popular substructuring methods: FETI-1, BDD, FETIDP, BDDC, and derive the primal versions to the two FETI methods, called P-FETI-1 and P-FETI-DP, as proposed by Fragakis and Papadrakakis. The formulation of the BDDC method shows that it is the same as P-FETI-DP and the same as a preconditioner introduced by Cros. We prove the equality of eigenvalues of a particular case of the FETI-1 method and of the BDD method by applying a recent abstract result by Fragakis.