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.

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

Summary: 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 
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     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},
     publisher = {mathdoc},
     volume = {15},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2003__15__a13/}
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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/