On the Equivalence of Primal and Dual Substructuring Preconditioners

Bedřich Sousedík; Jan Mandel

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arXiv · 0802.4328

On the Equivalence of Primal and Dual Substructuring Preconditioners

Bedřich Sousedík·Jan Mandel

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Abstract

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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Bedřich Sousedík, Jan Mandel. 2008-12-31. On the Equivalence of Primal and Dual Substructuring Preconditioners. https://arxiv.org/abs/0802.4328

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