Volume 15, pp. 18-28, 2003.

An additive Schwarz preconditioner for the spectral element ocean model formulation of the shallow water equations

Craig C. Douglas, Gundolf Haase, and Mohamed Iskandarani

Abstract

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.

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Key words

Shallow water equations, h-p finite elements, adaptive grids, multigrid, parallel computing, conjugate gradients, additive Schwarz preconditioner.

AMS subject classifications

68W10, 65Y05, 47N40, 76D33

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