Geodesic
Neumann-Neumann methods for vector field problems
Electronic transactions on numerical analysis, Tome 11 (2000), pp. 1-24.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we study some Schwarz methods of Neumann-Neumann type for some vector field problems, discretized with the lowest order Raviart-Thomas and N$\acute $ed$\acute $elec finite elements. We consider a hybrid Schwarz preconditioner consisting of a coarse component, which involves the solution of the original problem on a coarse mesh, and local ones, which involve the solution of Neumann problems on the elements of the coarse triangulation, also called substructures. We show that the condition number of the corresponding method is independent of the number of substructures and grows logarithmically with the number of unknowns associated with an individual substructure. It is also independent of the jumps of both the coefficients of the original problem. The numerical results presented validate our theoretical bound.
Classification : 65F10, 65N22, 65N30, 65N55
Keywords: edge elements, raviart-Thomas elements, domain decomposition, iterative substructuring, preconditioners, heterogeneous coefficients 
@article{ETNA_2000__11__a7,
     author = {Toselli, Andrea},
     title = {Neumann-Neumann methods for vector field problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {1--24},
     publisher = {mathdoc},
     volume = {11},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2000__11__a7/}
}
TY  - JOUR
AU  - Toselli, Andrea
TI  - Neumann-Neumann methods for vector field problems
JO  - Electronic transactions on numerical analysis
PY  - 2000
SP  - 1
EP  - 24
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ETNA_2000__11__a7/
LA  - en
ID  - ETNA_2000__11__a7
ER  - 
%0 Journal Article
%A Toselli, Andrea
%T Neumann-Neumann methods for vector field problems
%J Electronic transactions on numerical analysis
%D 2000
%P 1-24
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ETNA_2000__11__a7/
%G en
%F ETNA_2000__11__a7
Toselli, Andrea. Neumann-Neumann methods for vector field problems. Electronic transactions on numerical analysis, Tome 11 (2000), pp. 1-24. http://geodesic.mathdoc.fr/item/ETNA_2000__11__a7/