Geodesic
On the equivalence of primal and dual substructuring preconditioners
Electronic transactions on numerical analysis, Tome 31 (2008), pp. 384-402
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.
Classification : 65N55, 65M55, 65Y05
Keywords: domain decomposition methods, iterative substructuring, finite element tearing and interconnecting, balancing domain decomposition, BDD, BDDC, FETI, FETI-DP, P-FETI-DP 
@article{ETNA_2008__31__a1,
     author = {Soused{\'\i}k,  Bed\v{r}ich and Mandel,  Jan},
     title = {On the equivalence of primal and dual substructuring preconditioners},
     journal = {Electronic transactions on numerical analysis},
     pages = {384--402},
     year = {2008},
     volume = {31},
     zbl = {1189.65057},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__31__a1/}
}
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Sousedík,  Bedřich; Mandel,  Jan. On the equivalence of primal and dual substructuring preconditioners. Electronic transactions on numerical analysis, Tome 31 (2008), pp. 384-402. http://geodesic.mathdoc.fr/item/ETNA_2008__31__a1/