On the Equivalence of Primal and Dual Substructuring Preconditioners
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2009-09-30
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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
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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.