Geodesic
An additive Schwarz preconditioner for the spectral element ocean model formulation of the shallow water equations
Electronic transactions on numerical analysis, Tome 15 (2003), pp. 18-28
We discretize the shallow water equations with an Adams-Bashford scheme combined with the Crank-Nicholson scheme for the time derivatives and spectral elements for the discretization in space. The resulting coupled system of equations will be reduced to a Schur complement system with a special structure of the Schur complement. This system can be solved with a preconditioned conjugate gradients, where the matrix-vector product is only implicitly given. We derive an overlapping block preconditioner based on additive Schwarz methods for preconditioning the reduced system.
Classification : 68W10, 65Y05, 47N40, 76D33
Keywords: shallow water equations, h-p finite elements, adaptive grids, multigrid, parallel computing, conjugate gradients, additive Schwarz preconditioner 
@article{ETNA_2003__15__a13,
     author = {Douglas,  Craig C. and Haase,  Gundolf and Iskandarani,  Mohamed},
     title = {An additive {Schwarz} preconditioner for the spectral element ocean model formulation of the shallow water equations},
     journal = {Electronic transactions on numerical analysis},
     pages = {18--28},
     year = {2003},
     volume = {15},
     zbl = {1041.68127},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2003__15__a13/}
}
TY  - JOUR
AU  - Douglas,  Craig C.
AU  - Haase,  Gundolf
AU  - Iskandarani,  Mohamed
TI  - An additive Schwarz preconditioner for the spectral element ocean model formulation of the shallow water equations
JO  - Electronic transactions on numerical analysis
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UR  - http://geodesic.mathdoc.fr/item/ETNA_2003__15__a13/
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%0 Journal Article
%A Douglas,  Craig C.
%A Haase,  Gundolf
%A Iskandarani,  Mohamed
%T An additive Schwarz preconditioner for the spectral element ocean model formulation of the shallow water equations
%J Electronic transactions on numerical analysis
%D 2003
%P 18-28
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%U http://geodesic.mathdoc.fr/item/ETNA_2003__15__a13/
%G en
%F ETNA_2003__15__a13
Douglas,  Craig C.; Haase,  Gundolf; Iskandarani,  Mohamed. An additive Schwarz preconditioner for the spectral element ocean model formulation of the shallow water equations. Electronic transactions on numerical analysis, Tome 15 (2003), pp. 18-28. http://geodesic.mathdoc.fr/item/ETNA_2003__15__a13/