Geodesic
Multilevel preconditioners for Lagrange multipliers in domain imbedding
Electronic transactions on numerical analysis, Tome 15 (2003), pp. 94-105
A domain imbedding method where the Dirichlet boundary conditions are treated using boundary supported Lagrange multipliers is considered. The discretization leads to a saddle-point problem which is solved iteratively by using either the PMINRES method with a block-diagonal preconditioner or the PCG method in an Uzawa type approach. In both cases, the preconditioning of the Schur complement related to Lagrange multipliers is based on a special sparse implementation of BPX/MDS method. The developed preconditioning technique is wellsuited even for three-dimensional problems in domains with complicated shapes. Several numerical experiments for two-dimensional and three-dimensional problems demonstrate the efficiency and the applicability of the proposed method.
Classification : 65F10, 65N22, 65N55
Keywords: domain imbedding method, Lagrange multipliers, multilevel methods, preconditioning 
@article{ETNA_2003__15__a7,
     author = {Martikainen,  Janne and Rossi,  Tuomo and Toivanen,  Jari},
     title = {Multilevel preconditioners for {Lagrange} multipliers in domain imbedding},
     journal = {Electronic transactions on numerical analysis},
     pages = {94--105},
     year = {2003},
     volume = {15},
     zbl = {1030.65129},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2003__15__a7/}
}
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AU  - Martikainen,  Janne
AU  - Rossi,  Tuomo
AU  - Toivanen,  Jari
TI  - Multilevel preconditioners for Lagrange multipliers in domain imbedding
JO  - Electronic transactions on numerical analysis
PY  - 2003
SP  - 94
EP  - 105
VL  - 15
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LA  - en
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%A Rossi,  Tuomo
%A Toivanen,  Jari
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%J Electronic transactions on numerical analysis
%D 2003
%P 94-105
%V 15
%U http://geodesic.mathdoc.fr/item/ETNA_2003__15__a7/
%G en
%F ETNA_2003__15__a7
Martikainen,  Janne; Rossi,  Tuomo; Toivanen,  Jari. Multilevel preconditioners for Lagrange multipliers in domain imbedding. Electronic transactions on numerical analysis, Tome 15 (2003), pp. 94-105. http://geodesic.mathdoc.fr/item/ETNA_2003__15__a7/