On the Equivalence of Primal and Dual Substructuring Preconditioners

Details On the Equivalence of Primal and Dual Substructuring Preconditioners On the Equivalence of Primal and Dual Substructuring Preconditioners

2008-02-29

arxiv.org/abs/0802.4328v3

Electronic Transactions in Numerical Analysis 31, 384-402, 2008

Mathematics

Numerical Analysis

20 pages; typos corrected

Scientific paper

After a short historical review, we present four popular substructuring methods: FETI-1, BDD, FETI-DP, 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.

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