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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Published in Electronic Transactions on Numerical Analysis, v. 15, p. 18-28.

Copyright © 2003, Kent State University.

The copyright holders have granted the permission for posting the article here.

Funding Information

This research has been partially supported by NSF grants DMS-9707040, ACR-9721388, ACR-9814651, CCR- 9902022, and CCR-9988165, and National Computational Science Alliance grant OCE980001 (utilizing the University of Illinois Origin 2000 and the University of New Mexico Los Lobos systems).