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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.
Document Type
Article
Publication Date
2003
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).
Repository Citation
Douglas, Craig C.; Haase, Gundolf; and Iskandarani, Mohamed, "An Additive Schwarz Preconditioner for the Spectral Element Ocean Model Formulation of the Shallow Water Equations" (2003). Computer Science Faculty Publications. 10.
https://uknowledge.uky.edu/cs_facpub/10
Notes/Citation Information
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.